The valuative condition and R-Hopf algebra orders in KC p 3

Abstract

Let K be a finite extension of Q p endowed with the p-adic valuation and let R be its ring of integers. In this paper we give a complete classification of R-Hopf algebra orders in the group ring KC p 3 . For an arbitrary Hopf order H , we show that either the group scheme SpH or the group scheme SpH *, with H * the linear dual, can be viewed as the middle term of the Baer product of a distinguished extension with a generically trivial extension. Using this characterization we then compute algebra generators for either H or H *.