2012/11/19 by Aaron Michael Silberstein, Silberstein, Aaron Michael
Mathematics · #12F99 #14E20 #14H30 #20F34 #32Q55 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #Number Theory (math.NT) #math.AG #math.GR #math.GT #math.NT #msc:12F99 #msc:14E20 #msc:14H30 #msc:20F34 #msc:32Q55
paper · pdf · doi:10.48550/arxiv.1211.4608
30 pages, comments welcome!
openalex publication_date 2012/11/19 · arxiv created 2013/01/28 · arxiv updated 2013/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We finish the proof of the conjecture of F. Bogomolov and F. Pop: Let F1 and F2 be fields finitely-generated and of transcendence degree ≥ 2 over k1 and k2, respectively, where k1 is either ℚ or \mathbbFp, and k2 is algebraically closed. We denote by GF1 and GF2 their respective absolute Galois groups. Then the canonical map φ_F1, F2: \Isomi(F1, F2)→ \Isom\Out\cont(GF2, GF1) from the isomorphisms, up to Frobenius twists, of the inseparable closures of F1 and F2 to continuous outer isomorphisms of their Galois groups is a bijection. Thus, function fields of varieties of dimension ≥ 2 over algebraic closures of prime fields are anabelian. We apply this to give a necessary and sufficient condition for an element of the Grothendieck-Teichmüller group to be an element of the absolute Galois group of ℚ.