Finite descent obstruction for Hilbert modular varieties

2019/10/31 by Gregorio Baldi, Giada Grossi · 2 citations
Mathematics · #Advanced Algebra and Geometry #Algebra over a field #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Descent (aeronautics) #Mathematics #Modular design #Programming language #Pure mathematics #math.NT

paper · pdf · doi:10.4153/s0008439520000569

published in Canadian Mathematical Bulletin 64(2), 452-473 (Cambridge University Press) · To appear in Canadian Mathematical Bulletin

openalex publication_date 2020/07/22 · arxiv created 2020/08/06 · arxiv updated 2021/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Abstract Let S be a finite set of primes. We prove that a form of finite Galois descent obstruction is the only obstruction to the existence of \mathbb Z_S -points on integral models of Hilbert modular varieties, extending a result of D. Helm and F. Voloch about modular curves. Let L be a totally real field. Under (a special case of) the absolute Hodge conjecture and a weak Serre’s conjecture for mod ℓ representations of the absolute Galois group of L , we prove that the same holds also for the \mathcal O_L,S -points.

Citations

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