FoCM

Conference abstracts


Session S04 - Operator Algebras

July 26, 15:00 ~ 15:50

Nonarchimedean bornological algebras and their cyclic homology

Guillermo Cortiñas

Universidad de Buenos Aires, Argentina   -   gcorti@dm.uba.ar

Let V be a complete discrete valuation domain with maximal ideal πV, fraction field K=V[π1], and residue field k=V/πV. We are interested in developing a bivariant cohomology theory for k-algebras which takes values in K-vector spaces and has all the good properties (homotopy invariance, Morita invariance, excision, agreement with the relevant variant of de Rham cohomology in the commutative case, etc.). We assume that K has characteristic zero, but make no assumption on the characteristic of k; in fact the main case for us is char(k)=p>0. The general idea is to associate to each k-algebra A a (pro-) K-algebra T(A) and take (some variant of) the periodic cyclic homology of T(A). Such a construction already exists for commutative k-algebras of finite type; it yields Bertherlot's rigid cohomology, which is the correct variant of de Rham cohomology in this setting. In this talk I will explain a result we have interpreting rigid cohomology (made 2-periodic) of a commutative k-algebra A of finite type as the periodic cyclic homology of a certain pro-complete bornological K-algebra T(A). Along the way I will discuss bornological V and K-algebras,

Joint work with Joachim Cuntz (Universit\"at M\"unster) and Ralf Meyer (Universit\"at G\"ottingen).

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