Splinter-type conditions for classifying singularities

Abstract: The Direct Summand Theorem states that if $R$ is a commutative Noetherian ring, then any finite extension $R\to S$ splits as a map of $R$-modules. This suggests the notion of a splinter as a class of singularities, where we say a scheme $X$ is a splinter if, for any finite surjective map $\pi:Y\to X$ the natural map $\mathcal{O}_X\to\pi_*\mathcal{O}_Y$ splits as a map of $\mathcal{O}_X$-modules. In this talk, I'll discuss the history of using splinter-type conditions to classify singularities, including work of Bhatt and Kov\'acs, with the goal of introducing a recent result giving a splinter-type characterization of klt singularities.

algebraic geometrynumber theory

Audience: researchers in the discipline

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SFU NT-AG seminar

Series comments: The Number Theory and Algebraic Geometry (NT-AG) seminar is a research seminar dedicated to topics related to number theory and algebraic geometry hosted by the NT-AG group (Nils Bruin, Imin Chen, Stephen Choi, Katrina Honigs, Nathan Ilten, Marni Mishna).

We acknowledge the support of PIMS, NSERC, and SFU.

For Fall 2025, the organizers are Katrina Honigs and Peter McDonald.

We normally meet in-person in the indicated room. For online editions, we use Zoom and distribute the link through the mailing list. If you wish to be put on the mailing list, please subscribe to ntag-external using lists.sfu.ca

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