Speaker: Valerio Proietti (Univ. Oslo)

Title: The rational K-theory of ample groupoids

Date/Time: December 3 (Tue), 2024, 4:45-6:15pm

Room: 122 Math Sci Building (It will be also online. The Zoom link is the same as before. If you don't have one, please ask Kawahigashi.)

Abstract: Building on previous work by Davis and Luck, and recent constructions of KK-theory as a stable ‡-category, I will sketch the construction of a Chern character running from the left-hand side of the Baum-Connes conjecture for ample groupoids with torsion-free isotropy to the periodicized homology groups of the given groupoid. This map is a rational isomorphism, thereby establishing a modified form of Matuifs HK conjecture (after integral counterexamples have been found). This construction also computes the rational homotopy type of the algebraic K-theory spectrum of ample groupoids as defined in a recent work by X. Li. This is joint work-in-progress with M. Yamashita.