Standard Norm Varieties for Milnor Symbols mod p
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 cas...
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Veröffentlicht in: | arXiv.org 2015-11 |
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Format: | Artikel |
Sprache: | eng |
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Online-Zugang: | Volltext |
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Zusammenfassung: | 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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ISSN: | 2331-8422 |
DOI: | 10.48550/arxiv.1003.3971 |