New York Journal of Mathematics
Volume 23 (2017) 11-39


G. Griffith Elder and Robert G. Underwood

Finite group scheme extensions, and Hopf orders in KCp2 over a characteristic p discrete valuation ring

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Published: January 2, 2017
Keywords: Hopf orders, group schemes, extensions, cohomology groups
Subject: 16T05, 14L15, 20J05

Let p be prime. Let R be a discrete valuation ring of characteristic p with field of fractions K. Let Cp2 denote the elementary abelian group of order p2. In this paper we use Greither's approach for classifying short exact sequences of finite R-group schemes to classify R-Hopf orders H in the group ring KCp2, reproducing a result of Tossici. We then go further by providing an explicit description of the correspondence between these Hopf orders H and their duals H*, and also by explicitly describing their endomorphisms rings. Thus we are able to identify the Raynaud orders within this classification.

Author information

G. Griffith Elder:
Department of Mathematics, University of Nebraska at Omaha, Omaha, Nebraska, U.S.A.

Robert G. Underwood:
Department of Mathematics and Computer Science, Auburn University at Montgomery, Montgomery, Alabama, U.S.A