On the new theory of 1-motives

Abstract

This is a letter (not intended for publication in a regular journal) written in response to two referees of my preprint "Local duality theorems for commutative algebraic groups". In it, I discuss possible applications of the new theory of 1-motives introduced in that preprint. One of these is a new approach to the BSD conjecture for abelian varieties over global fields (developed here only partially) which builds on Bloch's well-known volume-theoretic interpretation of the conjecture in the number field case.