|タイトル||Reductions of Galois Representations of Small Slopes|
|講演者||Eknath Ghate 氏 (TIFR)|
|内容||It is a classical problem to compute the reductions of local Galois representations going back to Deligne (slope 0) and Fontaine (all positive slopes, but for small weights).
Breuil (and Berger and Colmez) revolutionized the subject by introducing a representation theoretic way to compute the reduction, via the introduction of p-adic and mod p Local Langlands Correspondences.
This method was used by Breuil himself to extend Fontaine's range of weights a bit for all positive slopes, and was then subsequently used by Buzzard-Gee to treat all weights, but for slopes in (0,1).
The speaker and several of his collaborators - Bhattacharya, Ganguli, Rozensztajn, Rai - have recently been involved in further extending the computation of the reduction for all slopes up to 2, again for all weights.
We explain some of the broad patterns that are emerging, along with some of the ingredients involved in the proof.