报告人：Hélène Esnault（Free University of Berlin）

时    间：2019-06-06  15:00-16:00

地    点：理科1号楼1114室

Abstract: We’ll review the classical vanishing theorems one has in algebraic geometry: Grothendieck’s vanishing theorem  for coherent cohomology, which implies via Artin-Schreier theory vanishing for étale cohomology with $\mathbb{F}_p$-coefficients in characteristic $p>0$, and Artin’s vanishing theorem for  étale cohomology with finite coefficients which are finite of order invertible on the variety. Recently Scholze formulated and proved a new kind of vanishing theorems which mixes Artin and Artin-Schreier theories, using his perfectoid methods. I’ll explain his theorem and how to prove it with different more classical methods.