Modul:   MAT770  Oberseminar: Algebraische Geometrie

On the field of meromorphic functions on a Stein compact set

Talk by Dr. Olivier Benoist

Speaker invited by: Prof. Dr. Joseph Ayoub

Date: 07.11.23  Time: 13.15 - 14.45  Room: Y27H25

I will prove that the field of meromorphic functions on a Stein compact set of dimension n (for instance on the closed unit ball in C^n) has cohomological dimension n. The main tool is an extension to the Stein setting of Artin’s theorem comparing étale and singular cohomology. I will give applications of these results to sums of squares problems in analytic geometry.