2010/03/31 by Dinh Huu Nguyen
Mathematics · #Algebra over a field #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Conjecture #Geometric and Algebraic Topology #Mod #Norm (philosophy) #Type (biology) #math.AG #math.KT
paper · pdf · doi:10.2140/akt.2016.1.457
published as AKT 1 (2016) 457-475 · submitted for publication
arxiv created 2015/11/12 · openalex created_date 2016/06/24 · openalex publication_date 2016/08/11 · arxiv updated 2016/08/31 · openalex updated_date 2026/08/05
We prove that the standard norm varieties for Milnor symbols mod [math] of length [math] are birationally isomorphic to Pfister quadrics when [math] , to Severi–Brauer varieties when [math] and [math] , and to varieties defined by reduced norms of cyclic algebras when [math] and [math] . In the case [math] and the case [math] and [math] , the results imply that the standard norm varieties for two equal Milnor symbols mod [math] are birationally isomorphic, and we conjecture this in general.