Rational points of quiver moduli spaces  [ Points rationnels des variétés de carquois ]
Annales de l'Institut Fourier, à paraître, 47 p.

Etant donné un corps parfait k et une clôture algébrique k ¯ de k, les espaces de modules de k ¯-représentations semistables d’un carquois Q sont des k-variétés algébriques dont nous étudions ici les propriétés arithmétiques, en particulier les points rationnels et leur interprétation modulaire. Outre les représentations à coefficients dans k, apparaissent naturellement certaines représentations rationnelles dites tordues, à coefficients dans une algèbre à division définie sur k et qui donnent lieu à différentes k-formes de la variété des modules initiale. En guise d’application, on montre qu’une k ¯-représentation stable du carquois Q est définissable sur une algèbre à division centrale bien précise, elle-même définie sur le corps des modules de la représentation considérée.

For a perfect base field k, we investigate arithmetic aspects of moduli spaces of quiver representations over k: we study actions of the absolute Galois group of k on the k ¯-valued points of moduli spaces of quiver representations over k and we provide a modular interpretation of the fixed-point set using quiver representations over division algebras, which we reinterpret using moduli spaces of twisted quiver representations (we show that those spaces provide different k-forms of the initial moduli space of quiver representations). Finally, we obtain that stable k ¯-representations of a quiver are definable over a certain central division algebra over their field of moduli.

Reçu le : 2018-04-10
Révisé le : 2019-03-07
Accepté le : 2019-09-18
Classification : 14D20,  14L24,  16G20
Mots clés: Problèmes de modules en géométrie algébrique, Théorie Géométrique des Invariants,Représentations de carquois
@unpublished{AIF_0__0_0_A18_0,
     author = {Hoskins, Victoria and Schaffhauser, Florent},
     title = {Rational points of quiver moduli spaces},
     note = {to appear in \emph{Annales de l'Institut Fourier}},
}
Hoskins, Victoria; Schaffhauser, Florent. Rational points of quiver moduli spaces. Annales de l'Institut Fourier, à paraître, 47 p.

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