## Algebraic Geometry Seminar

Javier Carvajal-Rojas

University of Utah

Fundamental groups of $F$-regular schemes and singularities

**Abstract:**In this talk I will start by summarizing recent work on the \'etale fundamental of $F$-regular singularities and schemes (joint work with subsets of B. Bhatt, P. Graf, K. Schwede and K. Tucker). After presenting some corollaries and a common limitation of these, I will discuss the necessity of considering a more general fundamental group, namely the Nori's fundamental group-scheme, which is well suited to the study of positive characteristic phenomena. As we will see, it gives a better understanding of the aforementioned corollaries. For example, we will see that the torsion, and not just the prime-to-$p$ torsion, of the Picard group of strongly $F$-regular singularities is bounded.

Wednesday March 1, 2017 at 4:00 PM in SEO 427