## 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.

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