## Algebraic K-Theory Seminar

Aron Heleodoro

Northwestern

Tensor product of Tate objects and higher adèles

**Abstract:**In this talk I will recall what Tate objects on a category C are and how one can endow them with a tensor operation, when C has a tensor structure. These operations however are not unique and their different choices are related to geometry. We will interpret these choices as flags in an algebraic variety by considering the very important example of (n-)Tate objects given by Beilinson-Parshin adèles. Finally, we will give an application of this tensor product to obtain a "local" decomposition of higher adèles in terms of 1-Tate objects. This talk is based on joint work with Braunling, Groechenig and Wolfson.

Wednesday November 1, 2017 at 10:30 AM in SEO 1227