Modul: MAT770 Oberseminar: Algebraische Geometrie

## A higher dimensional product formula for \(\ell\)-adic sheaves

Dr. Quentin Guignard talk

**Date:** 21.10.19 **Time:** 13.15 - 14.45 **Room:** Y27H25

The rank of the cohomology (or Euler characteristic) of an \(\ell\)-adic sheaf over a variety over a base field of characteristic prime to \(\ell\) is known to depend on the sheaf only through local invariants. We will explain why the same statement holds for the determinant of the cohomology, considered as a line with a Galois action. The local invariants whose product computes the determinant of the cohomology play the role of local epsilon factors in higher dimension.