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| Main Authors: | , |
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| Format: | Recurso digital |
| Language: | |
| Published: |
Zenodo
2025
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| Online Access: | https://doi.org/10.5281/zenodo.17711468 |
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Table of Contents:
- This paper explores the intricate local-global structure of p-adic Galois representations, fundamental objects in number theory connecting arithmetic and algebraic geometry. We analyze how their local behavior at p-adic fields constrains their global properties over number fields. The study synthesizes key theories, including the p-adic local Langlands correspondence, deformation theory of Galois representations, and p-adic Hodge theory, alongside classical conjectures like Fontaine-Mazur and Bloch-Kato, which establish precise links between local and global arithmetic invariants. We also discuss modern developments such as moduli stacks and shifted symplectic structures. This paper offers a concise overview of current understanding and open questions regarding the local-global compatibility of p-adic Galois representations, emphasizing their significance in the Langlands program.