On the section conjecture in anabelian geometry
ilustraciones, gráficas
- Autores:
-
Ríos Moreno, Andrés Ríos
- Tipo de recurso:
- Fecha de publicación:
- 2020
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/80630
- Palabra clave:
- 510 - Matemáticas
Geometry
Galois theory
Numbers, Theory of
Geometría
Teoría de Galois
Teoría de los números
Anabelian geometry
Section conjecture
Galois theory
Fundamental groups
Arithmetic geometry
Conjetura de secciones
Teoría de Galois
Grupos fundamentales
Geometría anabeliana
Geometría aritmética
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
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On the section conjecture in anabelian geometry |
| dc.title.translated.spa.fl_str_mv |
Sobre la conjetura de secciones en geometría anabeliana |
| title |
On the section conjecture in anabelian geometry |
| spellingShingle |
On the section conjecture in anabelian geometry 510 - Matemáticas Geometry Galois theory Numbers, Theory of Geometría Teoría de Galois Teoría de los números Anabelian geometry Section conjecture Galois theory Fundamental groups Arithmetic geometry Conjetura de secciones Teoría de Galois Grupos fundamentales Geometría anabeliana Geometría aritmética |
| title_short |
On the section conjecture in anabelian geometry |
| title_full |
On the section conjecture in anabelian geometry |
| title_fullStr |
On the section conjecture in anabelian geometry |
| title_full_unstemmed |
On the section conjecture in anabelian geometry |
| title_sort |
On the section conjecture in anabelian geometry |
| dc.creator.fl_str_mv |
Ríos Moreno, Andrés Ríos |
| dc.contributor.advisor.spa.fl_str_mv |
Cruz Morales, John Alexander |
| dc.contributor.author.spa.fl_str_mv |
Ríos Moreno, Andrés Ríos |
| dc.subject.ddc.spa.fl_str_mv |
510 - Matemáticas |
| topic |
510 - Matemáticas Geometry Galois theory Numbers, Theory of Geometría Teoría de Galois Teoría de los números Anabelian geometry Section conjecture Galois theory Fundamental groups Arithmetic geometry Conjetura de secciones Teoría de Galois Grupos fundamentales Geometría anabeliana Geometría aritmética |
| dc.subject.lemb.eng.fl_str_mv |
Geometry Galois theory Numbers, Theory of |
| dc.subject.lemb.spa.fl_str_mv |
Geometría Teoría de Galois Teoría de los números |
| dc.subject.proposal.eng.fl_str_mv |
Anabelian geometry Section conjecture Galois theory Fundamental groups Arithmetic geometry |
| dc.subject.proposal.spa.fl_str_mv |
Conjetura de secciones Teoría de Galois Grupos fundamentales Geometría anabeliana Geometría aritmética |
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ilustraciones, gráficas |
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2020 |
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2020-11 |
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2021-10-28T15:22:15Z |
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2021-10-28T15:22:15Z |
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Trabajo de grado - Maestría |
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info:eu-repo/semantics/masterThesis |
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Text |
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acceptedVersion |
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https://repositorio.unal.edu.co/handle/unal/80630 |
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Universidad Nacional de Colombia |
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Repositorio Institucional Universidad Nacional de Colombia |
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https://repositorio.unal.edu.co/ |
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https://repositorio.unal.edu.co/handle/unal/80630 https://repositorio.unal.edu.co/ |
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Universidad Nacional de Colombia Repositorio Institucional Universidad Nacional de Colombia |
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eng |
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eng |
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Balakrishnan, J. S., Dan-Cohen, I., Kim, M., Wewers, S. (2018). A non-abelian conjec- ture of Tateˆa€“Shafarevich type for hyperbolic curves. Mathematische Annalen, 372(1- 2), 369-428. Bombieri, E. (1990). The Mordell conjecture revisited. Annali della Scuola Normale Superiore di Pisa-Classe di Scienze, 17(4), 615-640. Deligne, P. (1980). La conjecture de Weil: II. Publications Math ́ematiques de l’IH ́eS, 52, 137-252. Esnault, H., Hai, P. H. (2008). Packets in Grothendieck’s section conjecture. Advances in Mathematics, 218(2), 395-416. Girondo, E., GonzA¡lez-Diez, G. (2012). Introduction to compact Riemann surfaces ̃ and dessins d’enfants (Vol. 79). Cambridge University Press. Grothendieck, A. (1958, August). The cohomology theory of abstract algebraic varieties. In Proceedings of the International Congress of Mathematicians (pp. 1) Grothendieck, A. (1983). Letter to Faltings. Geometric Galois Actions, 1. Grothendieck, A. (1997). Sketch of a Programme. Lond. Math. Soc. Lect. Note Ser, 242, 243-283. Grothendieck, A., Raynaud, M. (2002). Revˆetements ́etales et groupe fondamental (SGA 1). arXiv preprint math/0206203. Hartshorne, R. (2013). Algebraic geometry (Vol. 52). Springer Science Business Media. Hatcher, A. (2002). Algebraic Topology. Cambridge University Press. Ihara, Y. (1997). Some illustrative examples for anabelian geometry in high dimensions. London Math. Soc. Lect. Note Ser., 1, 127-138. Jacobson, N. (1964). Lectures In Abstract Algebra; Volume 3: Theory Of Fields And Galois Theory. Koenigsmann, J. (2005). On the section conjecture in anabelian geometry. Journal fur die reine und angewandte Mathematik, 2005(588), 221-235. Kock, B. (2001). Belyi’s theorem revisited. arXiv preprint math/0108222. Landesman, A. (2020). Invariance of the fundamental group under base change between algebraically closed fields. arXiv preprint arXiv:2005.09690. Lenstra, H. (2003). Profinite groups. Lecture notes available on the web. McLarty, C. (2007). The Rising Sea: Grothendieck on simplicity and generality. na. MAEHARA, K. (2001). Conjectures on birational geometry. The Academic Reports, the Faculty of Engineering, Tokyo Polytechnic University, 24(1), 9-18. Murre, J. P., Anantharaman, S. (1967). Lectures on an introduction to Grothendieck’s theory of the fundamental group. Bombay: Tata Institute of Fundamental Research. Marcus, D. A., Sacco, E. (1977). Number fields (Vol. 2). New York: Springer. Milne, J. S. (2009). Algebraic number theory (v3. 07). Milne, JS (1997). Class field theory. reading notes available at http: // www. math. lsa. umich. edu / jmilne . Milne, J. S. (1998). Lectures on ́etale cohomology. Available on-line at http://www. jmilne. org/math/CourseNotes/LEC. pdf. Milne, J. S., Milne, J. S. (1980). Etale cohomology (PMS-33) (Vol. 5657). Princeton university press. Mochizuki, S. (1996). The profinite Grothendieck conjecture for closed hyperbolic curves over number fields. Journal of Mathematical Sciences-University of Tokyo, 3(3), 571-628. Mochizuki, S. (1999). The local pro-p anabelian geometry of curves. Inventiones math- ematicae, 138(2), 319-423. Mochizuki, S. (2002). The absolute anabelian geometry of canonical curves. Kyoto Uni- versity. Research Institute for Mathematical Sciences [RIMS]. Mochizuki, S. (2003). Topics surrounding the anabelian geometry of hyperbolic curves. Galois groups and fundamental groups, Math. Sci. Res. Inst. Publ, 41, 119-165. Mochizuki, S. (2008). Topics in Absolute Anabelian Geometry: Generalities. I. Kyoto University, Research Institute for Mathematical Sciences. Mochizuki, S. (2013). Topics in absolute anabelian geometry II: decomposition groups and endomorphisms. J. Math. Sci. Univ. Tokyo, 20(2), 171-269. Mochizuki, S. (2015). Topics in absolute anabelian geometry III: global reconstruction algorithms. J. Math. Sci. Univ. Tokyo, 22(4), 939-1156. Nakamura, H. (1990). Galois rigidity of the ́etale fundamental groups of punctured projective lines. J. reine angew. Math, 411, 205-216. Nakamura, H. (1994). Galois rigidity of pure sphere braid groups and profinite calculus. J. Math. Sci. Univ. Tokyo, 1(1), 71-136. Nakamura, H. (1997). Galois rigidity of profinite fundamental groups. Sugaku Exposi- tions, 10(2). Nakamura, H., Tamagawa, A., Mochizuki, S. (2001). The conjecture on the fundamental groups of algebraic curves. Sugaku Expositions, 14(1), 31-54. Neukirch, J., Schmidt, A., Wingberg, K. (2013). Cohomology of number fields (Vol. 323). Springer Science Business Media. Neukirch, J. (2013). Algebraic number theory (Vol. 322). Springer Science Business Media. Neukirch, J. (1986). Class field theory (Vol. 280). Berlin: Springer. Oort, F. (1997). The algebraic fundamental group. LONDON MATHEMATICAL SO- CIETY LECTURE NOTE SERIES, 67-84. Poonen, B. (2017). Rational points on varieties (Vol. 186). American Mathematical Soc. Pop, F. (1990). On the Galois theory of function fields of one variable over number fields. J. reine angew. Math, 406, 200-218. Pop, F. (1994). On Grothendieck’s conjecture of birational anabelian geometry. Annals of Mathematics, 139(1), 145-182. Pop 4 Pop, F. (1997). Glimpses of Grothendieck’s anabelian geometry. London Mathematical Society Lecture Note Series, 113-126. Pop, F. (2005). Anabelian Phenomena in Geometry and Arithmetic. Lecture Notes of the AWS. Pop, F. (2010). On the birational p-adic section conjecture. Compositio Mathematica, 146(3), 621-637. Saidi, M. (2010). Good sections of arithmetic fundamental groups. arXiv preprint arXiv:1010.1313. Saidi, M. (2011). Around the Grothendieck anabelian section conjecture. Non-abelian Fundamental Groups and Iwasawa Theory, 393, 72. Szamuely, T. (2009). Galois groups and fundamental groups (Vol. 117). Cambridge University Press. Szamuely, T. (2012). Heidelberg lectures on fundamental groups. In The Arithmetic of Fundamental Groups (pp. 53-74). Springer, Berlin, Heidelberg. Schneps, L., Lochak, P. (Eds.). (1997). Geometric Galois actions: around Grothendieck’s esquisse d’un programme. Cambridge University Press. Serre, J. P. (2016). Topics in Galois theory. AK Peters/CRC Press. Silverman, J. H. (2009). The arithmetic of elliptic curves (Vol. 106). Springer Science Business Media. Stix, J. (2011). The Brauer Manin obstruction for sections of the fundamental group. Journal of Pure and Applied Algebra, 215(6), 1371-1397. Stix, J. (2012). Rational points and arithmetic of fundamental groups: Evidence for the section conjecture (Vol. 2054). Springer. Tamagawa, A. (1997). The Grothendieck conjecture for a ne curves. Compositio Math- ematica, 109(2), 135-194. Uchida, K. (1976). Isomorphisms of Galois groups. Journal of the Mathematical Society of Japan, 28(4), 617-620. Uchida, K. (1977). Isomorphisms of Galois groups of algebraic function fields. Annals of Mathematics, 106(3), 589-598. Uchida, K. (1981). Homomorphisms of Galois groups of solvably closed Galois exten- sions. Journal of the Mathematical Society of Japan, 33(4), 595-604. Uchida, K. (1982). Galois groups of unramified solvable extensions. Tohoku Mathemat- ical Journal, Second Series, 34(2), 311-317. Voevodsky, V. A. (1991). Galois representations connected with hyperbolic curves. Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 55(6), 1331-1342. |
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Universidad Nacional de Colombia |
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Departamento de Matemáticas |
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Atribución-NoComercial 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Cruz Morales, John Alexanderdccb3cd61bb5032b937ed55dad2c8138600Ríos Moreno, Andrés Ríos2dd342ec28bd0a79d4f0be08c5b345112021-10-28T15:22:15Z2021-10-28T15:22:15Z2020-11https://repositorio.unal.edu.co/handle/unal/80630Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/ilustraciones, gráficasIn this work, we study and present in detail some ground ideas of anabelian geometry, from its origin in number field and arithmetic results to the statements proposed by Grothendieck, studying theory of fundamental groups in algebraic geometry. We do emphasis in study of section conjecture.En este trabajo estudiamos y presentamos en detalle algunas ideas de geometría anabeliana, desde su origen en teoría de cuerpos y aritmética a los enunciados propuestos Grothendieck, estudiando la teoría de grupos fundamentales en geometría algebraica. Hacemos énfasis en estudiar la conjetura de secciones. (Texto tomado de la fuente).MaestríaMagíster en Ciencias - Matemáticasix, 96 páginasapplication/pdfengUniversidad Nacional de ColombiaBogotá - Ciencias - Maestría en Ciencias - MatemáticasDepartamento de MatemáticasFacultad de CienciasBogotá, ColombiaUniversidad Nacional de Colombia - Sede Bogotá510 - MatemáticasGeometryGalois theoryNumbers, Theory ofGeometríaTeoría de GaloisTeoría de los númerosAnabelian geometrySection conjectureGalois theoryFundamental groupsArithmetic geometryConjetura de seccionesTeoría de GaloisGrupos fundamentalesGeometría anabelianaGeometría aritméticaOn the section conjecture in anabelian geometrySobre la conjetura de secciones en geometría anabelianaTrabajo de grado - Maestríainfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/acceptedVersionTexthttp://purl.org/redcol/resource_type/TMBalakrishnan, J. S., Dan-Cohen, I., Kim, M., Wewers, S. (2018). A non-abelian conjec- ture of Tateˆa€“Shafarevich type for hyperbolic curves. Mathematische Annalen, 372(1- 2), 369-428.Bombieri, E. (1990). The Mordell conjecture revisited. Annali della Scuola Normale Superiore di Pisa-Classe di Scienze, 17(4), 615-640.Deligne, P. (1980). La conjecture de Weil: II. Publications Math ́ematiques de l’IH ́eS, 52, 137-252.Esnault, H., Hai, P. H. (2008). Packets in Grothendieck’s section conjecture. Advances in Mathematics, 218(2), 395-416.Girondo, E., GonzA¡lez-Diez, G. (2012). Introduction to compact Riemann surfaces ̃ and dessins d’enfants (Vol. 79). Cambridge University Press.Grothendieck, A. (1958, August). The cohomology theory of abstract algebraic varieties. In Proceedings of the International Congress of Mathematicians (pp. 1)Grothendieck, A. (1983). Letter to Faltings. Geometric Galois Actions, 1.Grothendieck, A. (1997). Sketch of a Programme. Lond. Math. Soc. Lect. Note Ser, 242, 243-283.Grothendieck, A., Raynaud, M. (2002). Revˆetements ́etales et groupe fondamental (SGA 1). arXiv preprint math/0206203.Hartshorne, R. (2013). Algebraic geometry (Vol. 52). Springer Science Business Media.Hatcher, A. (2002). Algebraic Topology. Cambridge University Press.Ihara, Y. (1997). Some illustrative examples for anabelian geometry in high dimensions. London Math. Soc. Lect. Note Ser., 1, 127-138.Jacobson, N. (1964). Lectures In Abstract Algebra; Volume 3: Theory Of Fields And Galois Theory.Koenigsmann, J. (2005). On the section conjecture in anabelian geometry. Journal fur die reine und angewandte Mathematik, 2005(588), 221-235.Kock, B. (2001). Belyi’s theorem revisited. arXiv preprint math/0108222.Landesman, A. (2020). Invariance of the fundamental group under base change between algebraically closed fields. arXiv preprint arXiv:2005.09690.Lenstra, H. (2003). Profinite groups. Lecture notes available on the web.McLarty, C. (2007). The Rising Sea: Grothendieck on simplicity and generality. na.MAEHARA, K. (2001). Conjectures on birational geometry. The Academic Reports, the Faculty of Engineering, Tokyo Polytechnic University, 24(1), 9-18.Murre, J. P., Anantharaman, S. (1967). Lectures on an introduction to Grothendieck’s theory of the fundamental group. Bombay: Tata Institute of Fundamental Research.Marcus, D. A., Sacco, E. (1977). Number fields (Vol. 2). New York: Springer.Milne, J. S. (2009). Algebraic number theory (v3. 07).Milne, JS (1997). Class field theory. reading notes available at http: // www. math. lsa. umich. edu / jmilne .Milne, J. S. (1998). Lectures on ́etale cohomology. Available on-line at http://www. jmilne. org/math/CourseNotes/LEC. pdf.Milne, J. S., Milne, J. S. (1980). Etale cohomology (PMS-33) (Vol. 5657). Princeton university press.Mochizuki, S. (1996). The profinite Grothendieck conjecture for closed hyperbolic curves over number fields. Journal of Mathematical Sciences-University of Tokyo, 3(3), 571-628.Mochizuki, S. (1999). The local pro-p anabelian geometry of curves. Inventiones math- ematicae, 138(2), 319-423.Mochizuki, S. (2002). The absolute anabelian geometry of canonical curves. Kyoto Uni- versity. Research Institute for Mathematical Sciences [RIMS].Mochizuki, S. (2003). Topics surrounding the anabelian geometry of hyperbolic curves. Galois groups and fundamental groups, Math. Sci. Res. Inst. Publ, 41, 119-165.Mochizuki, S. (2008). Topics in Absolute Anabelian Geometry: Generalities. I. Kyoto University, Research Institute for Mathematical Sciences.Mochizuki, S. (2013). Topics in absolute anabelian geometry II: decomposition groups and endomorphisms. J. Math. Sci. Univ. Tokyo, 20(2), 171-269.Mochizuki, S. (2015). Topics in absolute anabelian geometry III: global reconstruction algorithms. J. Math. Sci. Univ. Tokyo, 22(4), 939-1156.Nakamura, H. (1990). Galois rigidity of the ́etale fundamental groups of punctured projective lines. J. reine angew. Math, 411, 205-216.Nakamura, H. (1994). Galois rigidity of pure sphere braid groups and profinite calculus. J. Math. Sci. Univ. Tokyo, 1(1), 71-136.Nakamura, H. (1997). Galois rigidity of profinite fundamental groups. Sugaku Exposi- tions, 10(2).Nakamura, H., Tamagawa, A., Mochizuki, S. (2001). The conjecture on the fundamental groups of algebraic curves. Sugaku Expositions, 14(1), 31-54.Neukirch, J., Schmidt, A., Wingberg, K. (2013). Cohomology of number fields (Vol. 323). Springer Science Business Media.Neukirch, J. (2013). Algebraic number theory (Vol. 322). Springer Science Business Media.Neukirch, J. (1986). Class field theory (Vol. 280). Berlin: Springer.Oort, F. (1997). The algebraic fundamental group. LONDON MATHEMATICAL SO- CIETY LECTURE NOTE SERIES, 67-84.Poonen, B. (2017). Rational points on varieties (Vol. 186). American Mathematical Soc.Pop, F. (1990). On the Galois theory of function fields of one variable over number fields. J. reine angew. Math, 406, 200-218.Pop, F. (1994). On Grothendieck’s conjecture of birational anabelian geometry. Annals of Mathematics, 139(1), 145-182. Pop 4 Pop, F. (1997). Glimpses of Grothendieck’s anabelian geometry. London Mathematical Society Lecture Note Series, 113-126.Pop, F. (2005). Anabelian Phenomena in Geometry and Arithmetic. Lecture Notes of the AWS.Pop, F. (2010). On the birational p-adic section conjecture. Compositio Mathematica, 146(3), 621-637.Saidi, M. (2010). Good sections of arithmetic fundamental groups. arXiv preprint arXiv:1010.1313.Saidi, M. (2011). Around the Grothendieck anabelian section conjecture. Non-abelian Fundamental Groups and Iwasawa Theory, 393, 72.Szamuely, T. (2009). Galois groups and fundamental groups (Vol. 117). Cambridge University Press.Szamuely, T. (2012). Heidelberg lectures on fundamental groups. In The Arithmetic of Fundamental Groups (pp. 53-74). Springer, Berlin, Heidelberg.Schneps, L., Lochak, P. (Eds.). (1997). Geometric Galois actions: around Grothendieck’s esquisse d’un programme. Cambridge University Press.Serre, J. P. (2016). Topics in Galois theory. AK Peters/CRC Press.Silverman, J. H. (2009). The arithmetic of elliptic curves (Vol. 106). Springer Science Business Media.Stix, J. (2011). The Brauer Manin obstruction for sections of the fundamental group. Journal of Pure and Applied Algebra, 215(6), 1371-1397.Stix, J. (2012). Rational points and arithmetic of fundamental groups: Evidence for the section conjecture (Vol. 2054). Springer.Tamagawa, A. (1997). The Grothendieck conjecture for a ne curves. Compositio Math- ematica, 109(2), 135-194.Uchida, K. (1976). Isomorphisms of Galois groups. Journal of the Mathematical Society of Japan, 28(4), 617-620.Uchida, K. (1977). Isomorphisms of Galois groups of algebraic function fields. Annals of Mathematics, 106(3), 589-598.Uchida, K. (1981). Homomorphisms of Galois groups of solvably closed Galois exten- sions. Journal of the Mathematical Society of Japan, 33(4), 595-604.Uchida, K. (1982). Galois groups of unramified solvable extensions. Tohoku Mathemat- ical Journal, Second Series, 34(2), 311-317.Voevodsky, V. A. (1991). Galois representations connected with hyperbolic curves. Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 55(6), 1331-1342.Público generalLICENSElicense.txtlicense.txttext/plain; charset=utf-84074https://repositorio.unal.edu.co/bitstream/unal/80630/1/license.txt8153f7789df02f0a4c9e079953658ab2MD51ORIGINAL1015463368.2020.pdf1015463368.2020.pdfTesis de Maestría en Ciencias - Matemáticasapplication/pdf699398https://repositorio.unal.edu.co/bitstream/unal/80630/2/1015463368.2020.pdf6ee593fd7a657b68d14b7fa498204fe6MD52THUMBNAIL1015463368.2020.pdf.jpg1015463368.2020.pdf.jpgGenerated Thumbnailimage/jpeg3919https://repositorio.unal.edu.co/bitstream/unal/80630/3/1015463368.2020.pdf.jpg6eb223fe0a51a91b03998b73638b62edMD53unal/80630oai:repositorio.unal.edu.co:unal/806302023-07-30 23:04:06.751Repositorio Institucional Universidad Nacional de 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