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arXiv · 1003.3971

Standard Norm Varieties for Milnor Symbols mod p

Dinh Huu Nguyen
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Abstract

We prove that the standard norm varieties for Milnor symbols mod p of length n are birationally isomorphic to Pfister quadrics when p = 2, to Severi-Brauer varieties when p > 2, n = 2, and to varieties defined by reduced norms of cyclic algebras when p > 2, n = 3. In the case p = 2 and the case p > 2, n = 2, the results imply that the standard norm varieties for two equal Milnor symbols mod p are birationally isomorphic, and we conjecture this in general.

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Dinh Huu Nguyen. 2015-11-12. Standard Norm Varieties for Milnor Symbols mod p. https://doi.org/10.2140/akt.2016.1.457

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