Galois sections and p-adic period mappings

2022/04/28 by Betts, L. Alexander, Stix, Jakob · 2 citations
#14H25 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #Primary: 14H30. Secondary: 14G20

paper · doi:10.48550/arxiv.2204.13674

Abstract

Let K be a number field not containing a CM subfield. For any smooth projective curve Y/K of genus ≥2, we prove that the image of the "Selmer" part of Grothendieck's section set inside the K_v-rational points Y(K_v) is finite for every finite place v. This gives an unconditional verification of a prediction of Grothendieck's section conjecture. In the process of proving our main result, we also refine and extend the method of Lawrence and Venkatesh, with potential consequences for explicit computations.

Cited by

• Families of curves separating points
• On reductions of Selmer sections

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