Mod $p$ local-global compatibility for $\mathrm{GSp}_4(\mathbb{Q}_p)$ in the ordinary case
| Autor: | Enns, John, Lee, Heejong |
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| Rok vydání: | 2021 |
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| Druh dokumentu: | Working Paper |
| Popis: | Let $F$ be a totally real field of even degree in which $p$ splits completely. Let $\overline{r}:G_F \rightarrow \mathrm{GSp}_4(\overline{\mathbb{F}}_p)$ be a modular Galois representation unramified at all finite places away from $p$ and upper-triangular, maximally nonsplit, and of parallel weight at places dividing $p$. Fix a place $w$ dividing $p$. Assuming certain genericity conditions and Taylor--Wiles assumptions, we prove that the $\mathrm{GSp}_4(F_w)$-action on the corresponding Hecke-isotypic part of the space of mod $p$ automorphic forms on a compact mod center form of $\mathrm{GSp}_4$ with infinite level at $w$ determines $\overline{r}|_{G_{F_w}}$. Comment: Revised section 4.1 |
| Databáze: | arXiv |
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