학과 세미나 및 콜로퀴엄

구분 학과 세미나/콜로퀴엄
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제목 Towards a proof of the zig-zag conjecture (KAIX Invited Lecture)
Abstract The zig-zag conjecture predicts that the reductions of two-dimensional irreducible p-adic crystalline representations of half-integral slope and exceptional weights - weights which are two more than twice the slope modulo (p-1) - have reductions which are given by an alternating sequence of irreducible and reducible representations. Some partial progress was made towards this conjecture over the years by Buzzard-Gee (slope 1/2), Bhattacharya-G-Rozensztajn (slope 1) and G-Rai (slope 3/2). In this talk I shall use work of Breuil-Mézard and Guerberoff-Park in the semi-stable case and a limiting argument connecting crystalline and semi-stable representations due to Chitrao-G-Yasuda to show that zig-zag holds for half-integal slopes bounded by (p-1)/2, at least on the inertia subgroup, if the weight is sufficiently close to a weight bounded by p+1. (This is the first of the two KAIX Invited Lectures.)
일시 2022-11-08 (Tue) / 16:00 ~ 17:30
장소 E6,1401
강연언어 미정
강연자성명 Eknath Ghate
강연자소속 Tata Institute of Fundamental Research
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