2025/02/27 by Artusa, Marco · 1 citation
#11F85 (Secondary) #11S25 (Primary) #14F20 #14F45 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2502.19910
We extend Tate duality for Galois cohomology of abelian varieties to 1-motives over a p-adic field, improving a result of Harari and Szamuely. To do this, we replace Galois cohomology with the condensed cohomology of the Weil group. This is a topological cohomology theory defined in a previous work, which keeps track of the topology of the p-adic field. To see 1-motives as coefficients of this cohomology theory, we introduce their condensed Weil-étale realisation. Our duality takes the form of a Pontryagin duality between locally compact abelian groups.