北大数論セミナー：

Time： 16:30 – 17:30

Place：理学部3号館3-205室　　　

Speaker：Eknath Ghate 氏（タタ基礎研究所）

Title： Reductions of Galois representations using the Iwahori mod $p$ LLC

Abstract：We first recall the mod $p$ Local Langlands Correspondence using Iwahori induction. We then use the Iwahori mod $p$ LLC to compute the reductions of all 2-dimensional semi-stable representations of the Galois group of ${\mathbb Q}_p$ of weights up to $p + 1$.

We show that the reduction varies through an alternating sequence of irreducible and reducible representations. In the reducible cases, we also determine the tricky constants appearing in the unramified characters completely. This result allow us to complete our proof of our zig-zag conjecture in the crystalline world.

In principle, our method works for all weights. In particular, it lets
us go beyond the earlier glass ceiling of weight $p – 1$ which occurs in the deep work of Breuil-M\’ezard and Guerberoff-Park using methods from integral $p$-adic Hodge theory.

This is joint work with Anand Chitrao.

Organizers：朝倉 政典，蔡 園青，安田 正大