2018/10/31 by Federico Scavia
Mathematics · #Advanced Topology and Set Theory #Algebraic Geometry and Number Theory #Algebraic number #Mathematical and Theoretical Analysis #Multiplicative function #Noether's theorem #Prime (order theory) #Rationality #Retract #Type (biology) #math.AG #msc:11E72 #msc:14E08 #msc:20C10 #msc:20G15
paper · pdf · doi:10.4153/s0008439519000079
published as Can. Math. Bull. 63 (2020) 173-186
openalex created_date 2018/10/26 · openalex publication_date 2019/03/14 · arxiv created 2019/06/30 · arxiv updated 2020/02/19 · openalex updated_date 2026/08/05
Abstract For any prime number p and field k , we characterize the p -retract rationality of an algebraic k -torus in terms of its character lattice. We show that a k -torus is retract rational if and only if it is p -retract rational for every prime p , and that the Noether problem for retract rationality for a group of multiplicative type G has an affirmative answer for G if and only if the Noether problem for p -retract rationality for G has a positive answer for all p . For every finite set of primes S we give examples of tori that are p -retract rational if and only if p∉ S .