Project Details
Projekt
Computations of Chow-Witt groups for split quadrics and other smooth varieties
Subject Area
Mathematics
Term
from 2018 to 2021
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 405438664
Chow-Witt groups are refinements of the classical Chow groups. They contain important invariants of algebraic varieties. For example, they contain the "Euler class", which encodes the splitting behaviour of vector bundles over affine bases. The aim of this project is to compute the Chow-Witt groups of certain families of smooth varieties. Our initial focus will be on split quadrics, as results for these promise to have implications for the classical problem of the existence of sums-of-squares formulas. Next, we will investigate other classes of examples (other homogeneous spaces, smooth curves, ...). The Witt groups and the hermitian K-groups are already partially understood for these spaces, and the Chow-Witt groups are closely related to these via motivic spectral sequences.
DFG Programme
Priority Programmes
Subproject of
SPP 1786:
Homotopy Theory and Algebraic Geometry
