Speaker: Manav Batavia
Purdue University
Will give a Algebraic Geometry and Commutative Algebra Seminar entitled:
A sharp upper bound on cohomological dimension in unramified mixed characteristic
Abstract: Given an ideal I in a regular local ring A, the cohomological dimension of I in A is the index of the highest non-vanishing local cohomology of A supported at I. Determining effective upper bounds on the cohomological dimension in terms of topological invariants of Spec(A/I) is a central problem in commutative algebra: foundational results include the Hartshorne--Lichtenbaum Vanishing Theorem and the Second Vanishing Theorem. In equal characteristic, Faltings established in 1980 a general bound on the cohomological dimension of an ideal in terms of its “big height”. In this talk, we extend Faltings’ results to the unramified mixed characteristic setting and show that the resulting bound is sharp.
Date: 11-12-2026
Time: 3:30 pm
Location: 258 Hurley Hall