Presented By: Department of Mathematics
Commutative Algebra Seminar
A derived splinter characterization of klt singularities in characteristic zero
A ring R is a derived splinter if for every proper, surjective morphism $\pi:Y\to\Spec R$ the map $R\to R\pi_O_Y$ splits in the derived category of R-modules. Kovács has shown that in characteristic zero this is equivalent to R having rational singularities. In this talk, I’ll discuss how klt singularities, which are nicer than rational singularities, can be characterized in a similar fashion. Specifically, I’ll show that a ring R has kit-type if and only if, for all sufficiently large regular alterations $\pi:Y\to\Spec R$, there is a splitting of $R\to R\pi_O_Y$ that factors through $\pi_*\omega_Y$. Speaker(s): Peter McDonald (University of Utah)
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