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Finite descent obstruction for Hilbert modular varieties
- Part of
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- Journal:
- Canadian Mathematical Bulletin / Volume 64 / Issue 2 / June 2021
- Published online by Cambridge University Press:
- 22 July 2020, pp. 452-473
- Print publication:
- June 2021
-
- Article
- Export citation
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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 
$\ell $
representations of the absolute Galois group of L, we prove that the same holds also for the 
$\mathcal {O}_{L,S}$
-points.
