Related papers: Vanishing and injectivity theorems for Hodge modul…
We extend Igusa's map $\rho$ to modular forms which vanish on the hyperelliptic locus of the Siegel upper half-plane. The lowest non-vanishing derivatives of such modular forms are computed with the help of the general Thomae formula, they…
We prove Viehweg's hyperbolicity conjecture over compact bases and over bases with non-uniruled compactification. The most general case of the conjecture states that the the base space of a maximal variation family of smooth projective…
We present a simple alternative viewpoint on Hodge-Newton indecomposability, illustrating its explanatory value through a uniform proof of a combinatorial identity arising from affine Deligne-Lusztig varieties with finite Coxeter part.
The commutative and homological algebra of modules over posets is developed, as closely parallel as possible to the algebra of finitely generated modules over noetherian commutative rings, in the direction of finite presentations, primary…
In a previous paper, we stated a general almost purity theorem in the style of Faltings: if R is a ring for which the Frobenius maps on finite p-typical Witt vectors over R are surjective, then the integral closure of R in a finite \'etale…
After giving an explicit description of all the non vanishing Dolbeault cohomology groups of ample line bundles on grassmannians, I give two series of vanishing theorems for ample vector bundles on a smooth projective variety. They imply a…
In this paper we study rigid modules over commutative Noetherian local rings, establish new freeness criteria for certain periodic rigid modules, and extend several results from the literature. Along the way, we prove general Ext vanishing…
Using the framework of noncommutative Kahler structures, we generalise to the noncommutative setting the celebrated vanishing theorem of Kodaira for positive line bundles. The result is established under the assumption that the associated…
Various characterizations are offered of injectivity of the canonical fundamental group homomorphism for a certain class of inverse limit spaces. One application characterizes the existence of a kind of generalized universal cover.
We recall the construction of the Hodge character and we show, using a result due to F. Bittner, that these can be constructed using classical pure Hodge theory only, sideskipping Deligne's construction of functorial mixed Hodge structures…
In \cite{Broer1993}, it was shown that certain line bundles on $\widetilde{\mathcal{N}}=T^*G/B$ have vanishing higher cohomology. We prove a generalization of this theorem for real reductive algebraic groups. More specifically, if…
This article constructs Von Neumann invariants for constructible complexes and coherent D-modules on compact complex manifolds, generalizing the work of the author on coherent L 2-cohomology. We formulate a conjectural generalization of…
As is remarked by B. Totaro, R. Thomas essentially proved that the Hodge conjecture is inductively equivalent to the existence of a hyperplane section, called a generalized Thomas hyperplane section, such that the restriction to it of a…
We establish the Kodaira vanishing theorem and the Kawamata-Viehweg vanishing theorem for lc generalized pairs. As a consequence, we provide a new proof of the base-point-freeness theorem for lc generalized pairs. This new approach allows…
A result of H.-W. Wiesbrock is extended from the case of a common cyclic and separating vector for the half-sided modular inclusion of von Neumann algebras to the case of a common faithful normal semifinite weight and at the same time a gap…
Let k be a field of characteristic p>0. A theorem of de Jong shows that morphisms of modules over W(k)[[t]] with Frobenius and connection structure descend from the completion of W(k)((t)). A careful reading of de Jong's proof suggests the…
Musta\c{t}\u{a} a and Popa introduce the notion of Hodge ideals for an effective $\mathbb{Q}$-divisor $D$ and prove a vanishing theorem for Hodge ideals, which generalizes Nadel vanishing for multiplier ideals. However, their proof needs an…
We study the vanishing cycles of a one-parameter smoothing of a complex analytic space and show that the weight filtration on its perverse cohomology sheaf of the highest degree is quite close to the monodromy filtration so that its graded…
We develop the theory of Hodge ideals for Q-divisors by means of log resolutions, extending our previous work on reduced hypersurfaces. We prove local (non-)triviality criteria and a global vanishing theorem, as well as other analogues of…
The purpose of this paper is to study certain notions of metric positivity for the lowest nonzero piece in the Hodge filtration of a Hodge module. We show that the Hodge metric satisfies the minimal extension property. In particular, this…