Back to Commutative Algebra Seminar: Fall 2016
Commutative Algebra Seminar
Date: Friday, Sep 30, 2016
Time: 3:10PM - 4:00PM
Location: LCB 215
Javier Carvajal-Rojas
University of Utah
Title |
Fundamental groups of F-regular singularities via F-signature |
Abstract |
We will talk about the algebraic fundamental group of a strongly F-regular singularity. More concretely, via a new transformation rule for the F-signature under certain sort of mildly ramified finite extensions of rings, we will discuss the finiteness of these groups, analogous to results of Xu and Greb-Kebekus-Peternell for KLT singularities in characteristic zero. In contrast, our result and method are effective: we show that the reciprocal of the F-signature of the singularity gives a bound on the size of its fundamental group. As another consequence of these transformation rules, we also obtain purity of the branch locus over rings with mild singularities. Algebraic local fundamental groups will also be reviewed. This is joint work with Karl Schwede and Kevin Tucker. |
Commutative Algebra