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DTSTAMP;TZID=America/Vancouver:20221209T150000
DTSTART;TZID=America/Vancouver:20221209T150000
DTEND;TZID=America/Vancouver:20221209T155000

UID:20221209T150000@prima2022.primamath.org
SUMMARY:Coherent completeness in positive characteristic
DESCRIPTION: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 $[{\rm Spec} A/G]$ 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.  
STATUS:CONFIRMED
LOCATION:Finback
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