A generalization of the Cassels-Tate dual exact sequence

2006/08/23 by Cristian D. Gonzalez-Aviles, Gonzalez-Aviles, Cristian D., Ki-Seng Tan +1
Mathematics · #11G35 #14G25 #Commutative Algebra (math.AC) #FOS: Mathematics #Number Theory (math.NT) #math.AC #math.NT #msc:11G35 #msc:14G25

paper · pdf · doi:10.48550/arxiv.math/0608587

9 pages, 11 references

arxiv created 2006/08/23 · arxiv updated 2009/12/01

Abstract

We extend the well-known Cassels-Tate dual exact sequence for abelian varieties A over global fields K in two directions: we treat the p-primary component in the function field case, where p is the characteristic of K, and we dispense with the hypothesis that the Tate-Shafarevich group of A is finite.

Related

• The generalized Cassels-Tate dual exact sequence for 1-motives
• The Cassels-Tate pairing for finite Galois modules
• Tate Duality In Positive Dimension Over Function Fields
• Comparison of different Tate conjectures
• On geometric Brauer groups and Tate-Shafarevich groups