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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Accesso online: | https://arxiv.org/abs/2405.13250 |
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| _version_ | 1866911513198985216 |
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| author | Hernández, Jorge Alberto Robles Pérez-Buendía, J. Rogelio |
| author_facet | Hernández, Jorge Alberto Robles Pérez-Buendía, J. Rogelio |
| contents | This article, written in Spanish, provides a comprehensive review of the Fargues-Fontaine curve, a cornerstone in $p$-adic Hodge theory, and its pivotal role in classifying $p$-adic Galois representations. We synthesize key developments surrounding this curve, emphasizing its connection between advanced concepts in arithmetic geometry and the practical theory of representations. We offer a detailed analysis of the Fontaine period rings ($B_{cris}, B_{st}, B_{dR}$), exploring their crucial algebraic and arithmetic properties and their contribution to the curve's construction and definition. Furthermore, we delve into the theory of admissible $p$-adic Galois representations, discussing how the curve, once defined, integrates with Harder-Narasimhan theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_13250 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | La curva de Fargues--Fontaine: Una motivación al estudio de la teoría de representaciones de Galois $p$-ádicas Hernández, Jorge Alberto Robles Pérez-Buendía, J. Rogelio Number Theory Commutative Algebra Algebraic Geometry 11F85, 11S15, 11S20, 11F80 This article, written in Spanish, provides a comprehensive review of the Fargues-Fontaine curve, a cornerstone in $p$-adic Hodge theory, and its pivotal role in classifying $p$-adic Galois representations. We synthesize key developments surrounding this curve, emphasizing its connection between advanced concepts in arithmetic geometry and the practical theory of representations. We offer a detailed analysis of the Fontaine period rings ($B_{cris}, B_{st}, B_{dR}$), exploring their crucial algebraic and arithmetic properties and their contribution to the curve's construction and definition. Furthermore, we delve into the theory of admissible $p$-adic Galois representations, discussing how the curve, once defined, integrates with Harder-Narasimhan theory. |
| title | La curva de Fargues--Fontaine: Una motivación al estudio de la teoría de representaciones de Galois $p$-ádicas |
| topic | Number Theory Commutative Algebra Algebraic Geometry 11F85, 11S15, 11S20, 11F80 |
| url | https://arxiv.org/abs/2405.13250 |