Local-Global Structure of p-adic Galois Representations

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Autori principali: Revista, Zen, MATH, 10
Natura: Recurso digital
Pubblicazione: Zenodo 2025
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author Revista, Zen
MATH, 10
author_facet Revista, Zen
MATH, 10
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.
format Recurso digital
id zenodo_https___doi_org_10_5281_zenodo_17711468
institution Zenodo
language
publishDate 2025
publisher Zenodo
record_format zenodo
spellingShingle Local-Global Structure of p-adic Galois Representations
Revista, Zen
MATH, 10
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.
title Local-Global Structure of p-adic Galois Representations
url https://doi.org/10.5281/zenodo.17711468