2022/01/30 by Iyer, J. N., Parimala, R. · 1 citation
#14 F 22 #14 G 12 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2201.12780
Let C be a smooth projective curve of genus 2 over a number field k with a rational point. We prove that the index and exponent coincide for elements in the 2-torsion of \Sha(Br(C)). In the appendix, an isomorphism of the moduli space of rank 2 stable vector bundles with odd determinant on a smooth projective hyperelliptic curve C of genus g with a rational point over any field of characteristic not two with the Grassmannian of (g-1)-dimensional linear subspaces in the base locus of a certain pencil of quadrics is established, making a result of (\citeDe-Ra) rational. We establish a twisted version of this isomorphism and we derive as a consequence a weak Hasse principle for the smooth intersection X of two quadrics in \mathbb P5 over a number field: if X contains a line locally, then X has a k-rational point.