Franco-Asian Summer School on Arithmetic Geometry

Collection Franco-Asian Summer School on Arithmetic Geometry

Organisateur(s) Ahmed Abbes (CNRS & IHÉS), Ana Caraiani (Imperial College London ), Ariane Mézard (Sorbonne Université), Takeshi Saito (University of Tokyo), Takeshi Tsuji (The University of Tokyo), Daxin Xu (Chinese Academy of Sciences), Weizhe Zheng (Chinese Academy of Sciences).
Date(s) 30/05/2022 - 03/06/2022
URL associée https://www.ihes.fr/~abbes/Luminy/luminy2022.html
00:00:00 / 00:00:00
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Bounding the stalks of perverse sheaves in characteristic p via the characteristic cycle

De Will Sawin

The sheaf-function dictionary shows that many natural functions on the F_q-points of a variety over F_q can be obtained from l-adic sheaves on that variety. To obtain upper bounds on these functions, it is necessary to obtain upper bounds on the dimension of the stalks of these sheaves. In many number theory problems, the functions we need to bound arise from perverse sheaves. David Massey proved an upper bound for the dimension of a stalk of a perverse sheaf in terms of an intersection-theoretic invariant of the characteristic cycle called a polar multiplicity. Unfortunately, he proved this only over the complex numbers, making it unusable for these problems. I will explain how to rectify this by proving an analogous statement over finite fields. This has applications to function field analogues of three problems in number theory: The Michel-Venkatesh conjecture about equidistribution of CM points, a question about large values of automorphic forms, and the number of primes in an arithmetic progression.

Informations sur la vidéo

  • Date de captation 03/06/2022
  • Date de publication 20/06/2022
  • Institut IHES
  • Langue Anglais
  • Audience Chercheurs, Doctorants
  • Format MP4
  • Lieu CIRM

Document(s)

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