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This article gives a description, by means of functorial intrinsic fibrations, of the
geometric structure (and conjecturally also of the Kobayashi pseudometric, as well as of
the arithmetic in the projective case) of compact Kähler manifolds. We first define
special manifolds as being the compact Kähler manifolds with no meromorphic map onto an
orbifold of general type, the orbifold structure on the base being given by the divisor
of multiple fibres. We next show that rationally connected Kähler...
For any compact Kähler manifold and for any equivalence relation generated by a
symmetric binary relation with compact analytic graph in , the existence of a
meromorphic quotient is known from Inv. Math. 63 (1981). We give here a simplified
and detailed proof of the existence of such quotients, following the approach of that
paper. These quotients are used in one of the two constructions of the core of given
in the previous paper of this fascicule, as well as in many other questions.
A “relative” -theory group for holomorphic or algebraic vector bundles on a compact or quasiprojective complex manifold is constructed, and Chern-Simons type characteristic classes are defined on this group in the spirit of Nadel. In the projective case, their coincidence with the Abel-Jacobi image of the Chern classes of the bundles is proved. Some applications to families of holomorphic bundles are given and two Riemann-Roch type theorems are proved for these classes.
On donne des propriétés de la catégorie tannakienne des modules de Dieudonné filtrés sur un corps -adique (ces modules de Dieudonné jouent en -adique un rôle analogue aux structures de Hodge complexes). On prouve l’existence d’un foncteur fibre sur et la simple connexité du groupe associé. Ceci permet de montrer, sous la conjecture de Fontaine : “faiblement admissible entraîne admissible”, une conjecture de Rapoport et Zink décrivant le torseur entre cohomologie cristalline et étale, et de prouver...
Un résultat de positivité de théorie de Hodge nous permet de déterminer certaines pôles de la distribution pour une fonction analytique à singularité isolée. Dans le cas des courbes et des singularités quasi-homogènes on détermine l’ensemble exact des pôles. On démontre aussi que si le résidu d’une forme holomorphe est de carré intégrable sur la fibre spéciale, l’intégrale sur la fibre spéciale est limite de celle sur les fibres voisines.
We recall some basic constructions from -adic Hodge theory, then describe some recent results in the subject. We chiefly discuss the notion of -pairs, introduced recently by Berger, which provides a natural enlargement of the category of -adic Galois representations. (This enlargement, in a different form, figures in recent work of Colmez, Bellaïche, and Chenevier on trianguline representations.) We also discuss results of Liu that indicate that the formalism of Galois cohomology, including Tate...
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