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An exact sequence for Milnor's K-theory with applications to quadratic forms

Dmitry Orlov·Alexander Vishik·Vladimir Voevodsky
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Abstract

We construct a four-term exact sequence which provides information on the kernel and cokernel of the multiplication by a pure symbol in Milnor's K-theory mod 2 of fields of characteristic zero. As an application we establish, for fields of characteristics zero, the validity of three conjectures in the theory of quadratic forms - the Milnor conjecture on the structure of the Witt ring, the Khan-Rost-Sujatha conjecture and the J-filtration conjecture. The first version of this paper was written in the spring of 1996.

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Dmitry Orlov, Alexander Vishik, Vladimir Voevodsky. 2001-01-03. An exact sequence for Milnor's K-theory with applications to quadratic forms. https://doi.org/10.4007/annals.2007.165.1

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