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arXiv · 2409.07923

The section conjecture for the toric fundamental group over $p$-adic fields

Giulio Bresciani
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Abstract

Loosely speaking, the toric fundamental group is the Tannaka dual of a category of vector bundles which become direct sums of line bundles on a finite étale cover. In characteristic $0$, it is an extension of the étale fundamental group scheme by a projective limit of tori. We prove the analogue of Grothendieck's section conjecture for the toric fundamental group over $p$-adic fields. As a consequence, we give a new interpretation of Selmer sections as toric Galois sections.

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Giulio Bresciani. 2026-09-14. The section conjecture for the toric fundamental group over $p$-adic fields. https://arxiv.org/abs/2409.07923

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