Shravan Patankar : Singularities in Mixed Characteristic (after Ma and Schwede)

Posted by Benjamin Gould , part of the Graduate Algebraic Geometry Seminar.

At

Dec. 9, 2020, 11 a.m.

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Zoom

Abstract

In her thesis, Karen Smith showed that a singularity in characteristic zero is rational provided its `reduction' to a prime which is `large enough' is F-rational. Astonishingly, using recent advances in mixed characteristic commutative algebra, Ma and Schwede show that the former is true for *any* prime p. Apart from being of independent interest, this has substantial algorithmic consequences to determine whether a char 0 singularity is rational. We will isolate the part of the above proposition which requires `perfectoid theory' and study their general `spreading out' technique which has its roots in a first course in algebraic geometry.