On Hilbert Satz 90 for K3 for degree-two extensions

by Markus Rost (Preprint, May 86, 14 pages)

The text describes a proof of Hilbert's Satz 90 for K3 for quadratic extensions.

The results had been obtained independently by A. Merkurjev and A. Suslin, see

The two proofs differ significantly concerning the investigation of the residue maps on K_3 of the function field of a conic. While Merkurjev and Suslin use here their general results about indecomposable K_3, our method consists in specific considerations of conics. We use Rehmann's description of K2 of skew fields and the Reidemeister-Schreier method to obtain a rational parametrization of generators and relations for K2 of a quaternion algebra.

For the final conclusion one uses also the preprint Injectivity of K2(D) -> K2(F) for quaternion algebras. An "elementary" proof of the result can be found in the preprint On Hilbert Satz 90 for K3 for quadratic extensions.

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