Vol. 1, No. 4, 2016

Download this article
Download this article For screen
For printing
Recent Issues
Volume 4, Issue 2
Volume 4, Issue 1
Volume 3, Issue 4
Volume 3, Issue 3
Volume 3, Issue 2
Volume 3, Issue 1
Volume 2, Issue 4
Volume 2, Issue 3
Volume 2, Issue 2
Volume 2, Issue 1
Volume 1, Issue 4
Volume 1, Issue 3
Volume 1, Issue 2
Volume 1, Issue 1
The Journal
About the Journal
Subscriptions
Editorial Board
Ethics Statement
Submission Guidelines
Submission Form
Editorial Login
Ethics Statement
Author Index
To Appear
Contacts
ISSN: 2379-1691 (e-only)
ISSN: 2379-1683 (print)
Other MSP Journals
Standard norm varieties for Milnor symbols mod $p$

Dinh Huu Nguyen

Vol. 1 (2016), No. 4, 457–475
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 and n = 2, and to varieties defined by reduced norms of cyclic algebras when p > 2 and n = 3. In the case p = 2 and the case p > 2 and 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.

Keywords
algebraic geometry, Milnor K-theory, Milnor symbols, norm varieties, standard norm varieties, generic splitting varieties, $p$-generic splitting varieties, norm variety, standard norm variety, generic splitting variety, $p$-generic splitting variety
Mathematical Subject Classification 2010
Primary: 14E99, 19E99
Milestones
Received: 26 August 2015
Revised: 19 October 2015
Accepted: 3 November 2015
Published: 11 August 2016
Authors
Dinh Huu Nguyen
Department of Mathematics
UCLA
Los Angeles, CA 90095
United States