Javier Carvajal-Rojas : Fundamental groups of $F$-regular schemes and singularities

Posted by Kevin Tucker , part of the Algebraic Geometry Seminar.

At

March 1, 2017, 4 p.m.

In

SEO 427

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.