Characteristic Cycle and Estimates for the Betti Numbers of Étale Sheaves

by Jean-Baptiste Teyssier (Sorbonne Université)

Thursday Mar 27, 2025, 11:00 AM → 12:30 PM Europe/Paris

Amphithéâtre Léon Motchane (IHES)

Séminaire de géométrie arithmétique

Let U be a smooth variety over an algebraically closed field k of characteristic p > 0 and let X be a smooth compactification of U where D := X - U is an effective Cartier divisor. To an l-adic local system L on U, Abbes and Saito attached a conductor c(L) measuring the wild ramification of L at the generic points of D. In this talk, we will advertise the existence of a polynomial P depending only on X such that the Betti numbers of every l-adic local system L on U are bounded by rk(L) P(c(L)). We will underline the role played by Saito's characteristic cycle and explain how these bounds can be extended to constructible complexes on arbitrary schemes of finite type over k. If time permits, we will explain some arithmetic and geometric consequences for the étale fundamental group. This is joint work with Haoyu Hu. 

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