CAPITAL REGION ALGEBRA/NUMBER THEORY SEMINAR Speaker: Lindsay Childs, Univ. at Albany Time: Wednesday, April 2, at 4:30pm Place: Bailey Hall 100, Union College Title: Duality for Hopf orders Abstract: Let R be the valuation ring of K, a finite field extension of Q_p, and let G be a cyclic group of p-power order. If L is a totally and wildly ramified Galois extension of K with Galois group G and valuation ring S, and if the associated order A of L/K (that is, the set of elements of KG that multiply S to S) is a Hopf order, then S is a free A-module. That fact motivates the problem of describing (classifying) Hopf orders over R in KG. We shall survey what is known and unknown on this problem. The most recent results are joint work with Rob Underwood. Refreshments at 4:15pm in Math. Dept. Lounge, 2nd floor.