2019/09/06 by Gonzalez-Aviles, Cristian D.
#14G25 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #Primary 11G25
paper · doi:10.48550/arxiv.1909.03125
Let K be a global field, let S be a finite set of primes of K containing the archimedean primes and let A be an abelian variety over K. We generalize the duality theorem established in our paper "On Neron class groups of abelian varieties" by removing the hypothesis in [op.cit.] that the Tate-Shafarevich group of A is finite. We also derive an exact sequence that relates the indicated group associated to the Jacobian variety of a proper, smooth and geometrically connected curve X over K to a certain finite subquotient of the Brauer group of X. The sequence alluded to above may be regarded as a global analog of an exact sequence of S.Biswas.