On the new theory of 1-motives

2024/01/31 by Gonzalez-Aviles, Cristian D.
#11G25 #14G20 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2401.17960

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.

Related

• Local-global principles for 1-motives
• The generalized Cassels-Tate dual exact sequence for 1-motives
• Abelian motives and Shimura varieties in nonzero characteristic
• Arithmetic duality theorems for 1-motives over function fields
• Local duality theorems for commutative algebraic groups