Algebraic Geometry Seminar
Jarod Alper
University of Washington Seattle
Coherent completeness in positive characteristic
Abstract: Grothendieck's Existence Theorem asserts that a coherent sheaf on a scheme proper over a complete local noetherian ring is the same as a compatible system of coherent sheaves on the thickenings of its central fiber. This is a fundamental result with important applications to moduli theory. We will discuss generalizations of this result to algebraic stacks beginning with a review of the characteristic 0 situation where a satisfactory answer is known: any quotient stack [Spec A/G] whose invariant ring A^G is a complete local k-algebra is coherently complete along its unique closed point. We will report on partial progress in joint work with Hall and Lim on extending this result to positive characteristic.
Monday October 24, 2022 at 3:00 PM in 636 SEO