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Despite the failure of the integral Hodge conjecture, we show that the rational Hodge conjecture implies an integral version (modulo torsion) of the absolute Hodge conjecture.

In this article we develop a unified framework for proving Morita invariance of cohomology theories associated to Lie groupoids. Our approach is to view these cohomology theories as arising from sheaves of modules on the nerve of the…

For modular indecomposable representations of a cyclic group $G$ of prime order $p$ we propose a list of polynomial invariants of degree $\leq 3$ that, together with a simple invariant of degree $p$, separate generic orbits and generate the…

Given a two-dimensional conformal field theory with a global symmetry, we propose a method to implement an orbifold construction by taking orbits of the modular group. For the case of cyclic symmetries we find that this approach always…

In this paper we discuss generalized group, provides some interesting examples. Further we introduce a generalized module as a module like structure obtained from a generalized group and discuss some of its properties and we also describes…

We construct Hodge filtered cohomology groups for complex manifolds that combine the topological information of generalized cohomology theories with geometric data of Hodge filtered holomorphic forms. This theory provides a natural…

We investigate various topological spaces and varieties which can be associated to a block of a finite group scheme G. These spaces come from the theory of cohomological support varieties for modules, as well as from the…

We prove a local-global principle for torsors under the prosolvable geometric fundamental group of an affine curve over a number field.

A generalization of the Hartogs theorem is proved for a class of Tubes structures. We assume that the intervening commutative Lie algebra admits at least a number of globally solvable generators greater or equal to the structure…

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…

In this note we discuss local gauge-invariant operators in noncommutative gauge theories. Inspired by the connection of these theories with the Matrix model, we give a simple construction of a complete set of gauge-invariant operators. We…

In this work in progress, we discuss independence and interpolation and related topics for classical, modal, and non-monotonic logics.

This paper studies Moore's measurable cohomology theory for locally compact groups and Polish modules. An elementary dimension-shifting argument is used to show that all classes in that theory have representatives with considerable extra…

In the derived category of modules over a commutative noetherian ring a complex $G$ is said to generate a complex $X$ if the latter can be obtained from the former by taking summands and finitely many cones. The number of cones required in…

In the first part of this paper, we consider, in the context of an arbitrary hyperplane arrangement, the map between compactly supported cohomology to the usual cohomology of a local system. A formula (i.e., an explicit algebraic de Rham…

Suppose that Y is a cyclic cover of projective space branched over a hyperplane arrangement D, and that U is the complement of the ramification locus in Y. The first theorem implies that the Beilinson-Hodge conjecture holds for U if certain…

We study the generic Hodge groups $\Hg(\sX)$ of local universal deformations $\sX$ of Calabi-Yau 3-manifolds with onedimensional complex moduli, give a complete list of all possible choices for $\Hg(\sX)_{\R}$ and determine the latter real…

We explain a correct proof of the decomposition theorem for direct images of constant Hodge modules by proper K\"ahler morphisms of complex manifolds. We also give some examples showing certain difficulty in the non-constant Hodge module…

We use techniques of Alper-Hall-Rydh to prove a local structure theorem for smooth morphisms between smooth stacks around points with linearly reductive stabilizers. This implies that the good moduli space of a smooth stack over a base has…

We present a general and comprehensive overview of recent developments in the theory of integral models of Shimura varieties of Hodge type. The paper covers the following topics: construction of integral models, their possible moduli…