Overconvergent cohomology, $p$-adic $L$-functions and families for $\mathrm{GL}(2)$ over CM fields
| Autor: | Salazar, Daniel Barrera, Williams, Chris |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | J. Th\'eor. Nomb. Bordeaux, 33 (2021), no.3, pp.659-701 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.5802/jtnb.1175/ |
| Popis: | The use of overconvergent cohomology in constructing $p$-adic $L$-functions, initiated by Stevens and Pollack--Stevens in the setting of classical modular forms, has now been established in a number of settings. The method is compatible with constructions of eigenvarieties by Ash--Stevens, Urban and Hansen, and is thus well-adapted to non-ordinary situations and variation in $p$-adic families. In this note, we give an exposition of the ideas behind the construction of $p$-adic $L$-functions via overconvergent cohomology. Conditional on the non-abelian Leopoldt conjecture, we illustrate them by constructing $p$-adic $L$-functions attached to families of base-change automorphic representations for $\mathrm{GL}(2)$ over CM fields. As a corollary, we prove a $p$-adic Artin formalism result for base-change $p$-adic $L$-functions. Comment: 31 pages, final version. To appear in Journal de Theorie des Nombres de Bordeaux (Iwasawa 2019 special issue) |
| Databáze: | arXiv |
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