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- W4386869534 abstract "The notion of companions has been defined by Deligne (Publ Math IHÉS 52:137–252, 1980, Conjecture 1.2.10) who predicted its existence. We report on the ( $$ell $$ -adic version) of it (L. Lafforgue (Invent Math 147(1):1–241, 2002, Théorème VII.6) in dimension 1, Drinfeld (Moscow Math J 12(3):515–542, 2012, Theorem 1.1) in higher dimension in the smooth case), explain how we used Drinfeld’s theorem in the proof of Simpson’s integrality conjecture for cohomologically rigid complex local systems in Esnault and Groechenig (Sel Math 24(5):4279–4292, 2018, Theorem 1.1), also why we proceeded like this, and how we combined this idea together with de Jong’s conjecture in order to define and obtain an integrability property of the Betti moduli space (de Jong and Esnault, Integrality of the Betti moduli space, 18 pp. Trans. AMS, to appear, Theorem 1.1)." @default.
- W4386869534 created "2023-09-20" @default.
- W4386869534 creator A5073683726 @default.
- W4386869534 date "2023-01-01" @default.
- W4386869534 modified "2023-09-27" @default.
- W4386869534 title "Lecture 7: Companions, Integrality of Cohomologically Rigid Local Systems and of the Betti Moduli Space" @default.
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- W4386869534 doi "https://doi.org/10.1007/978-3-031-40840-3_7" @default.
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