5:00PM: Absolute integral closure in characteristic pDavid BerlekampLet R be a local Noetherian domain of positive characteristic. A theorem of Hochster and Huneke shows that the absolute integral closure of R is CohenMacaulay if R is excellent. The existence of big CohenMacaulay algebras is one of the homological conjectures, and indeed rather a strong one; it implies, for instance, the monomial conjecture (if x_1, ..., x_d is a system of parameters, then (x_1x_2...x_d)^n is not in the ideal generated by the (n+1)th powers of the x_i, for any n). I will present a simpler proof of this result, given by Huneke and Lyubeznik, which extends to the case where R is the image of a Gorenstein local ring, and elaborate somewhat on these connections.
