$L$-complete Hopf algebroids and their comodules

Details $L$-complete Hopf algebroids and their comodules $L$-complete Hopf algebroids and their comodules

2009-01-11

arxiv.org/abs/0901.1471v4

Mathematics

Algebraic Topology

Substantial revision with improvements in some results and proofs. New appendix on non-exactness of tensorproducts with pro-fr

Scientific paper

We investigate Hopf algebroids in the category of $L$-complete modules over a commutative Noetherian regular complete local ring. The main examples are provided by the Hopf algebroids associated to Lubin-Tate spectra in the K(n)-local stable homotopy category and we show that these have Landweber filtrations for all finitely generated discrete modules. Along the way we investigate the canonical Hopf algebras associated to Hopf algebroids over fields and introduce a notion of unipotent Hopf algebroid generalising that for Hopf algebras. In two appendices we continue the discussion of the connections with twisted group rings, and expand on a result of Hovey on the non-exactness of coproducts of L-complete modules.

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