Back to Algebraic Geometry Seminar: Fall 2023
Algebraic Geometry Seminar
Date: Tuesday, Oct 17, 2023
Time: 3:30PM - 4:30PM
Location: LCB 323
Charles Vial
Universität Bielefeld
Title |
On proper splinters in positive characteristic |
Abstract |
A commutative ring is called a splinter if any finite-module ring extension splits. By the direct summand conjecture, now a theorem due to André, every regular ring is a splinter. The notion of splinter can naturally be extended to schemes. In that context, every normal scheme in characteristic zero is a splinter. In contrast, Bhatt observed in his thesis that the splinter property for proper schemes in positive characteristic imposes strong constraints on the global geometry; for instance, the structure sheaf of a proper splinter in positive characteristic has vanishing positive-degree cohomology. I will report on joint work with Johannes Krah where we describe further restrictions on the global geometry of proper splinters in positive characteristic. |
Algebraic Geometry