L-complete Hopf algebroids

Andy Baker (Glasgow)

Wednesday 11th February, 2009 16:00-17:00 Mathematics Building, room 214

Abstract

Let R be a commutative ring and I an ideal (things work best when R is regular and I is maximal). Then the I-adic completion functor is not left or right exact on R-modules. Its left derived functors L_* were studied by Greenlees & May. In particular, if the natural map M->L_0M is an isomorphism, M is called L-complete. The full subcategory L-Mod_R of Mod_R consisting of L-complete modules is symmetric monoidal. I will review some of the properties of L-Mod_R. Hopf algebroids are cogroupoid objects in the category of commutative rings. I will discuss a notion of L-complete Hopf algebroid and comodules over such objects. In good cases, finitely generated L-complete comodules have Jordan-Holder filtrations. The motivation for much of this lies in algebraic topology

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