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Charles Vial, Universität Bielefeld 
Wednesday 12 November 2025, 14:15-15:15
On proper splinters in positive characteristic
- 👤 Speaker: Charles Vial, Universität Bielefeld 🔗 Website
- 📅 Date & Time: Wednesday 12 November 2025, 14:15 - 15:15
- 📍 Venue: CMS MR13
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, a scheme in characteristic zero is a splinter if and only if it is normal. 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, and where we also address the derived-invariance of the (derived-)splinter property.
Series This talk is part of the Algebraic Geometry Seminar series.
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