On Tannakian duality over valuation rings

[摘要] In this paper we generalize the Tannakian theory which gives a correspondence between groupoids and Tannakian categories over a field k to the case where k is a valuation ring. We give a general theorem how to reconstruct groupoids in arbitrary categories from their category of representations and we show that this theorem can be applied to groupoids over Dedekind rings. We also give a partial answer how to see whether a category is the representation category of a groupoid over a valuation ring. (C) 2004 Elsevier Inc. All rights reserved.

[发布日期] 2004-12-15