|Date: Thursday, November 09, 2017
Location: 4088 East Hall (3:00 PM to 4:00 PM)
Title: A Zariski-Nagata theorem in mixed characteristic
Abstract: One version of a classical result by Zariski and Nagata describes symbolic powers in polynomial rings over the complex numbers in terms of differential operators. Namely, the n-th symbolic power of a prime consists of the elements such that each differential operator of order at most n-1 sends the element into the prime ideal. This is known hold in polynomial rings over perfect fields, but fails in mixed characteristic. In this paper, we use p-derivations, a notion due to Buium and Joyal, to define a new kind of differential powers in mixed characteristic, and prove that this new object does coincide with the symbolic powers of prime ideals. This is joint work with Alessandro De Stefani and Eloisa Grifo.
Speaker: Jack Jeffries
Institution: University of Michigan