Distinguished Colloquium——On some vanishing theorems in algebraic geometry
报告人：Hélène Esnault (Free University of Berlin)
时间：2019-06-06 15:00-16:00
地点：Room 1114, Sciences Building No. 1
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.
