Local-Global Structure of p-adic Galois Representations
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| Autori principali: | , |
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| Natura: | Recurso digital |
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Zenodo
2025
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| _version_ | 1866901724646604800 |
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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 |