Anderson T-motives and abelian varieties with MIQF: results coming from an analogy

2009/07/27 by Grishkov, A., Logachev, D.
#11G09 #11G10 #11G15 #14K99 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.0907.4712

Abstract

Analogy between Anderson T-motives and abelian varieties with multiplication by an imaginary quadratic field (MIQF) is a source of 2 results: 1. A description of abelian varieties with MIQF of dimension r and signature (n, r-n) in terms of "lattices" of dimension r in \Bbb Cⁿ; 2. A construction of exterior powers of abelian varieties with MIQF having n=1.

Related

• Introduction to Anderson t-motives: a survey
• Pure Anderson Motives and Abelian Sheaves over Finite Fields
• Abelian motives and Shimura varieties in nonzero characteristic
• On CM abelian varieties over imaginary quadratic fields
• An inductive approach to the Hodge conjecture for abelian varieties