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Bibliographic Details
Main Authors: Hernández, Jorge Alberto Robles, Pérez-Buendía, J. Rogelio
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2405.13250
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Table of 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.