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Connected Hopf corings and their Dieudonné counterparts

2014; Springer Nature; Volume: 3; Issue: 3 Linguagem: Inglês

10.1007/s40065-014-0109-2

2193-5343

Rui Miguel Saramago,

Advanced Topics in Algebra

We define coring objects in the category of algebras over a perfect field of characteristic p (with connected underlying Hopf algebra) and the corresponding notion for Dieudonné modules, and prove the equivalence of the two resulting categories, extending thus the methods of Dieudonné theory for Hopf rings from Ravenel (Reunión Sobre Teoría de Homotopía, volume 1 of Serie notas de matemática y simposia, 177–194, 1975), Schoeller (Manusc Math 3:133–155, 1970), Goerss (Homotopy invariant algebraic structures: a conference in honor of J. Michael Boardman, 115–174, 1999) and Saramago (Dieudonné theory for ungraded and periodically graded Hopf rings, Ph.D. thesis, The Johns Hopkins University, 2000).