English

Standard Norm Varieties for Milnor Symbols mod p

Algebraic Geometry 2016-08-31 v3 K-Theory and Homology

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.

Cite

@article{arxiv.1003.3971,
  title  = {Standard Norm Varieties for Milnor Symbols mod p},
  author = {Dinh Huu Nguyen},
  journal= {arXiv preprint arXiv:1003.3971},
  year   = {2016}
}

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R2 v1 2026-06-21T15:00:19.839Z