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Finite descent obstruction for Hilbert modular varieties
Published online by Cambridge University Press: 22 July 2020
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
$\ell $
representations of the absolute Galois group of L, we prove that the same holds also for the
$\mathcal {O}_{L,S}$
-points.
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- © Canadian Mathematical Society 2020
Footnotes
This work was supported by the Engineering and Physical Sciences Research Council [EP/ L015234/1], the EPSRC Centre for Doctoral Training in Geometry and Number Theory (The London School of Geometry and Number Theory), and University College London.
References
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