Graduate Algebraic Geometry Seminar
Shravan Patankar
Singularities in Mixed Characteristic (after Ma and Schwede)
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.
Wednesday December 9, 2020 at 11:00 AM in Zoom