PIMS MSS Colloquium: Anne Quéguigner-Mathieu

Quadratic form theory started as a part of number theory; people were notably interested in representation questions, such as which number of a given field can be written as a sum of a certain number of squares. In the 1930’s, Witt started the algebraic theory of quadratic forms: besides working over a general field F, he considered the set of all quadratic forms, and built the so-called Witt ring of F. More recently, the study of correspondences on smooth projective varieties, and in particular on quadrics, renewed the theory, and led to significant results on very classical questions. \

The purpose of this talk is to introduce an important tool in the geometric theory of quadratic forms, namely the Chow motive of a quadric, and relate it to classical notions, via a famous theorem due to Vishik.