Crossed product and hereditary orders

Abstract

Let be the crossed product order (O L /O K , G,p) where L/K is a finite Galois extension of local fields with Galois group G, and p is a factor set with values in 0*. Let o = , and let /+1 be the left order O^rad A,) of rad A r The chain of orders o , A l9 ... 9 A s ends with a hereditary order A s . We prove that A s is the unique minimal hereditary order in A = KA containing A, that A s has e/m simple modules, each of dimension / over the residue class field K of O , and that s = d -(e -1). Here d,e,f are the different exponent, ramification index, and inertial degree of L/K, and m is the Schur index of A.