SFU Number Theory and Algebraic Geometry Seminar: Peter McDonald

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.