Title: Hochster's formula for local cohomology, part 2

Abstract: Let (V,t) be a discrete valuation ring with fraction field L and residue field K. A t-Stanley Reisner ring is the image of a Stanley-Reisner ring over V under the evaluation map sending x_0 to t; these are quotients of polynomial rings by ideals whose generators are square free "t-monomials," i.e. monomials in the variables and the uniformizing parameter t. There is a correspondence between t-Stanley Reisner rings and simplicial complexes with a distinguished vertex v_0. As is the case for classical Stanley-Reisner rings, this correspondence induces many deep connections between algebra and topology. The theory is particularly rich and nuanced when the simplicial complex has p-torsion, where (V,t) is a ring of mixed characteristic p. In this talk, we will discuss the adaptation of Hochster's formula to t-Stanley-Reisner rings. Instead of using simplicial cohomology over a fixed coefficient ring, we will need to consider "cellular sheaf cohomology." The cellular sheaf assigns one of L, V, or K to each face, depending on its proximity to the distinguished vertex v_0.