Student Arithmetic Geometry Seminar: Log étale fundamental groups and families

Seminar | September 15 | 4:10-5 p.m. | 740 Evans Hall

 Martin Olsson, UCB

 Department of Mathematics

If $A$ is a complete noetherian local ring with residue field $k$ and $X/A$ is a proper $A$-scheme with closed fiber $X_k$, then the Grothendieck existence theorem implies that the reduction functor on categories of finite étale covers $$ \text {Fet}(X)\rightarrow \text {Fet}(X_k) $$ is an equivalence of categories. In this talk I will explain a logarithmic version and discuss some applications.