2012/03/19 by Aravind Asok
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Class (philosophy) #Cohomology #Commutative Algebra and Its Applications #Conjecture #Counterexample #Generalization #Polynomial and algebraic computation #Prime (order theory) #Torsion (gastropod) #Variety (cybernetics) #math.AG #math.KT
paper · pdf · doi:10.1112/s0010437x13007021
published as Compositio Math. 149 (2013) 1312-1326 · 15 pages; Revised and extended version of http://arxiv.org/abs/1001.4574 v2; Comments welcome!
arxiv created 2012/03/19 · openalex publication_date 2013/06/03 · openalex created_date 2016/06/24 · arxiv updated 2019/02/20 · openalex updated_date 2026/08/04
Abstract We show how the techniques of Voevodsky’s proof of the Milnor conjecture and the Voevodsky–Rost proof of its generalization the Bloch–Kato conjecture can be used to study counterexamples to the classical Lüroth problem. By generalizing a method due to Peyre, we produce for any prime number ℓ and any integer n≥ 2 , a rationally connected, non-rational variety for which non-rationality is detected by a non-trivial degree n unramified étale cohomology class with ℓ -torsion coefficients. When ℓ = 2 , the varieties that are constructed are furthermore unirational and non-rationality cannot be detected by a torsion unramified étale cohomology class of lower degree.