THE HOMOTOPY K-THEORY FOR NON-ARCHIMEDEAN BORNOLOGICAL ALGEBRAS

Speaker(s)

DEVARSHI MUKHERJEE

Affiliation

Universidad de Buenos Aires, Argentina

Date

May 10, 2023, 5:15 p.m.

Information about the event

405 IMPAN & ZOOM

Seminar

North Atlantic Noncommutative Geometry Seminar

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I will define non-Archimedean bivariant K-theory. This is the target of the universal functor on the category of complete, torsion free bornological Zp-algebras that satisfies homotopy invariance, stability and excision, and is a non-Archimedean analogue of Cuntz's kk-theory for locally convex algebras. Since analytic and (rationalised) periodic cyclic homology are also functors satisfying this property, the universal property yields bivariant Chern characters between bivariant K-theory and bivariant analytic cyclic homology. Finally, we show that when the first variable is the ground ring Zp, bivariant K-theory yields a version of Weibel's homotopy algebraic K-theory.

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