Abstract
Witt groups of fields were introduced by Ernst Witt in the 1930s. Witt groups have been found very useful for studying quadratic forms over fields in the 1960s. In the 1970s, Knebusch introduced Witt groups of algebraic schemes using the language of Grothendieck, and he proposed to compute Witt groups of smooth projective quadrics. In this talk, I will construct an exact sequences connecting Witt groups of smooth projective quadrics and Clifford algebras. This exact sequence has an immediate application to Witt kernel of functions fields of quadrics，which relates to the problem of solving one quadratic equation with many variables.
