Abstract
We show that the action of Hecke operators away from p on the space of (p-adic) overconvergent modular forms is (p-adically) locally analytic in a certain sense. As a corollary, the action of the Hecke algebra can be extended naturally to an action of rigid functions on its generic fiber. This directly determines the Hodge–Tate–Sen weights of Galois representation associated to an overconvergent eigenform and confirms a conjecture of Gouvêa.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 3297-3311 |
| Number of pages | 15 |
| Journal | Journal of the European Mathematical Society |
| Volume | 27 |
| Issue number | 8 |
| DOIs | |
| State | Published - 2025 |
All Science Journal Classification (ASJC) codes
- General Mathematics
- Applied Mathematics
Keywords
- fake-Hasse invariants
- locally analytic action
- overconvergent modular forms
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