##### Department of Mathematics,

University of California San Diego

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### Southern California Algebraic Geometry Seminar

## Anastasia Stavrova

#### Fields Institute

## Isotropic reductive groups and non-stable K-theory

##### Abstract:

A semisimple (more generally, reductive) group scheme is called isotropic, if it contains a proper parabolic subgroup. In particular, the special orthogonal group of a non-degenerate quadratic form is isotropic if and only if the form itself is isotropic. To any isotropic reductive group G over a commutative ring R one associates a group-valued functor $K_1^G$ on the category of commutative R-algebras, which is an analog of the non-stable $K_1-functor GL_n/E_n$. When R is a field, $K_1^G$ coincides on smooth algebras with the group of $A^1$-connected components of G in the sense of Morel-Voevodsky. We will discuss various properties of these functors, and connections with classification of principal G-bundles.

Host: Dragos Oprea

### April 13, 2013

### 3:30 PM

### AP&M 6402

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