The Brauer-Manin obstruction for constant curves over global function fields

2019/09/22 by Creutz, Brendan, Voloch, José Felipe · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1909.10102

Abstract

Let \mathbbF be a finite field and C,D smooth, geometrically irreducible proper curves over \mathbbF and set K = \mathbbF(D). We consider Brauer-Manin and abelian descent obstructions to the existence of rational points and to weak approximation for the curve C ⊗_\mathbbF K. In particular, we show that Brauer-Manin is the only obstruction to weak approximation and the Hasse principle in the case that the genus of D is less than that of C. We also show that we can identify the points corresponding to non-constant maps D → C using Frobenius descents.

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• Adelic Mordell-Lang and the Brauer-Manin obstruction

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