Seminar Event Detail

Commutative Algebra

Date:  Thursday, April 14, 2022
Location: (password: algebra) Virtual East Hall (4:00 PM to 5:00 PM)

Title:  A derived splinter characterization of klt singularities in characteristic zero

Abstract:   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:  Peter McDonald
Institution:  University of Utah

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