Geodesic
Finite descent obstruction for Hilbert modular varieties
Canadian mathematical bulletin, Tome 64 (2021) no. 2, pp. 452-473

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DOI

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.
DOI : 10.4153/S0008439520000569
Mots-clés : Hilbert modular varieties, descent obstruction, Galois representations, Serre’s conjecture, Abelian varieties of GL2-type, totally real fields 
Baldi, Gregorio; Grossi, Giada. Finite descent obstruction for Hilbert modular varieties. Canadian mathematical bulletin, Tome 64 (2021) no. 2, pp. 452-473. doi: 10.4153/S0008439520000569
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     title = {Finite descent obstruction for {Hilbert} modular varieties},
     journal = {Canadian mathematical bulletin},
     pages = {452--473},
     year = {2021},
     volume = {64},
     number = {2},
     doi = {10.4153/S0008439520000569},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439520000569/}
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