Zig-zag for Galois Representations
| Autor: | Ghate, Eknath |
|---|---|
| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | The zig-zag conjecture says that the reductions of two-dimensional crystalline representations of the Galois group of ${\mathbb {Q}}_p$ of large exceptional weights and half-integral slopes up to $\frac{p-1}{2}$ vary through an alternating sequence of irreducible and reducible mod $p$ representations. We prove this conjecture in smoothly varying families of such representations for $p \geq 5$. The proof uses a limiting argument due to Chitrao-Ghate-Yasuda to reduce to the case of semi-stable representations of weights at most $p+1$, and then appeals to the work of Breuil-M\'ezard, Guerberoff-Park and Chitrao-Ghate. Comment: Updated version: title changed to reflect that this version contains a proof of the conjecture on the full Galois group not just on the inertia subgroup; also includes a proof for the top two slopes |
| Databáze: | arXiv |
| Externí odkaz: |
|