Uniform bounds and ultraproducts of cycles

2009/01/30 by Lars Brünjes, Brünjes, Lars, Christian Serpé +1
Mathematics · #14F20 (Secondary) #14G13 (Primary) 14C25 #Algebraic Geometry (math.AG) #FOS: Mathematics #Logic (math.LO) #math.AG #math.LO #msc:14C25 #msc:14F20 #msc:14G13

paper · pdf · doi:10.48550/arxiv.0901.4853

11 pages

arxiv created 2009/01/30 · arxiv updated 2009/12/01

Abstract

This paper is about the question whether a cycle in the l-adic cohomology of a smooth projective variety over the rational numbers, which is algebraic over almost all finite fields, is also algebraic over the rationals. We use ultraproducts respectively nonstandard techniques in the sense of A. Robinson, which the authors applied systematically to algebraic geometry. We give a reformulation of the question in form of uniform bounds for the complexity of algebraic cycles over finite fields.

Related

• Cycle conjectures and birational invariants over finite fields
• Etale and motivic cohomology and ultraproducts of schemes
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• Autour de la conjecture de Tate `a coefficients Z_l pour les vari'et'es sur les corps finis
• On analogues of the Kato conjectures and proper base change for 1-cycles on rationally connected varieties