代数学コロキウム

過去の記録 ~04/13次回の予定今後の予定 04/14~

開催情報 水曜日 17:00~18:00 数理科学研究科棟(駒場) 117号室
担当者 今井 直毅,ケリー シェーン

今後の予定

2024年04月17日(水)

17:00-18:00   数理科学研究科棟(駒場) 117号室
Ahmed Abbes 氏 (IHES、東大数理(日本学術振興会 外国人招へい研究者))
Functoriality of the p-adic Simpson correspondence by proper push forward (English)
[ 講演概要 ]
Faltings initiated in 2005 a p-adic analogue of the (complex) Simpson correspondence whose construction has been taken up by various authors, according to several approaches. After recalling the one initiated by myself with Michel Gros, I will present our initial result on the functoriality of the p-adic Simpson correspondence by proper push forward, leading to a generalization of the relative Hodge-Tate spectral sequence. If time permits, I will give a brief overview of an ongoing project with Michel Gros and Takeshi Tsuji, aimed at establishing a more robust framework for achieving broader functoriality results of the p-adic Simpson correspondence, by both proper push forward and pullback.

2024年05月01日(水)

17:00-18:00   数理科学研究科棟(駒場) 117号室
松本晃二郎 氏 (東京大学大学院数理科学研究科)
On the potential automorphy and the local-global compatibility for the monodromy operators at p ≠ l over CM fields. (日本語)
[ 講演概要 ]
Let F be a totally real field or CM field, n be a positive integer, l be a prime, π be a cohomological cuspidal automorphic representation of GLn over F and v be a non-l-adic finite place of F. In 2014, Harris-Lan-Taylor-Thorne constructed the l-adic Galois representation corresponding to π. (Scholze also constructed this by another method.) The compatibility of this construction and the local Langlands correspondence at v was proved up to semisimplification by Ila Varma(2014), but the compatibility for the monodromy operators was known only in conjugate self-dual cases and some special 2-dimensional cases. In this talk, we will prove the local-global compatibility in some self-dual cases and sufficiently regular weight cases by using some new potential automorphy theorems. Moreover, if we have time, we will also prove the Ramanujan conjecture for the cohomological cuspidal automorphic representations of GL2 over F, which was proved in parallel weight cases by Boxer-Calegari-Gee-Newton-Thorne (2023).

2024年05月08日(水)

17:00-18:00   数理科学研究科棟(駒場) 117号室
Xinyao Zhang 氏 (東京大学大学院数理科学研究科)
The pro-modularity in the residually reducible case (English)
[ 講演概要 ]
For a continuous odd two dimensional Galois representation over a finite field of characteristic p, it is conjectured that its universal deformation ring is isomorphic to some p-adic big Hecke algebra, called the big R=T theorem. Recently, Deo explored the residually reducible case and proved a big R=T theorem for Q under the assumption of the cyclicity of some cohomology group. However, his method is unavailable for totally real fields since the assumption does not hold any longer. In this talk, we follow the strategy of the work from Skinner-Wiles and Pan on the Fontaine-Mazur conjecture and give a pro-modularity result for some totally real fields, which is an analogue to the big R=T theorem.