# Talk

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.