We give a simple proof of a result originally due to Dimca and Suciu: a group that is both Kähler and the fundamental group of a closed three-manifold is finite. We also prove that a group that is both the fundamental group of a closed three-manifold and of a non-Kähler compact complex surface is or .
The paper is devoted to algebraic surfaces which can be obtained using a simple combinatorial procedure called the T-construction. The class of T-surfaces is sufficiently rich: for example, we construct T-surfaces of an arbitrary degree in RP³ which are M-surfaces. We also present a construction of T-surfaces in RP³ with dim H1 (RX; Z/2) > h1, 1(CX), where RX and CX are the real and the complex point sets of the surface.
Nous étudions dans cet article les représentations cristallines vérifiant les conditions de Fontaine-Laffaille, en particulier l’image de l’inertie modérée. A partir de cette image, nous définissons un tore et une représentation de ce tore, dont nous montrons qu’elle est à valeurs (sous certaines conditions) dans l’adhérence de Zariski de l’image de la représentation galoisienne, et nous donnons le lien entre cette représentation du tore et le groupe à un paramètre de Hodge-Tate (tout ceci à l’aide...
Let be a Henselian discrete valuation ring with field of fractions . If is a smooth variety over and a torus over , then we consider -torsors under . If is a model of then, using a result of Brahm, we show that -torsors under extend to -torsors under a Néron model of if is split by a tamely ramified extension of . It follows that the evaluation map associated to such a torsor factors through reduction to the special fibre. In this way we can use the geometry of the special...