Related papers: Some Hodge theory from Lie algebras
We investigate the Friedman--Goldfarb--Harrington theorem from two perspectives. Firstly, in the frameworks of classical and modal propositional logics, we study the forms of sentences whose existence is guaranteed by the FGH theorem.…
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.
The equations obeyed by the vacuum expectation value of the Wilson loop of Abelian gauge theories are considered from the point of view of the loop-space. An approximative scheme for studying these loop-equations for lattice Maxwell theory…
In this article, we pursue two main objectives. The first is to show that the fundamental results of Green-Lazarsfeld (1987, 1991) on generic vanishing theorems, and works of Budur-Wang (2015, 2020) on cohomology jumping loci, can be…
We prove many cases of a conjecture of Buzzard, Diamond and Jarvis on the possible weights of mod $p$ Hilbert modular forms, by making use of modularity lifting theorems and computations in $p$-adic Hodge theory.
We construct correspondences in logarithmic Hodge theory over a perfect field of arbitrary characteristic. These are represented by classes in the cohomology of sheaves of differential forms with log poles and, notably, log zeroes on…
$p$-adic Hodge Theory is one of the most powerful tools in modern Arithmetic Geometry. In this survey, we will review $p$-adic Hodge Theory for algebraic varieties, present current developments in $p$-adic Hodge Theory for analytic…
The paper is devoted to a generalized and improved version of author's approach to Gromov bounded cohomology theory. In particular, the awkward countability assumption is removed and the aspects related to homological algebra are clarified.…
We review the recent development of Hodge theory for almost complex manifolds. This includes the determination of whether the Hodge numbers defined by $\bar\partial$-Laplacian are almost complex, almost K\"ahler, or birational invariants in…
We construct motives over the rational numbers associated with symmetric power moments of Kloosterman sums, and prove that their L-functions extend meromorphically to the complex plane and satisfy a functional equation conjectured by…
The purpose of this paper is to introduce a cohomology theory for abelian matched pairs of Hopf algebras and to explore its relationship to Sweedler cohomology, to Singer cohomology and to extension theory. An exact sequence connecting…
A cohomology theory of the adjoint of Hopf algebras, via deformations, is presented by means of diagrammatic techniques. Explicit calculations are provided in the cases of group algebras, function algebras on groups, and the bosonization of…
This paper gives a $p$-adic analogue of the Mackey theory, which relates representations of a group of type $G=H\times_{t} A $ to systems of imprimitivity.
We extend the relative theory of admissible pairs and $p$-adic Hodge structures introduced in Part II to allow variation in the underlying local systems of $\mathbb{Q}_p$-vector spaces and isocrystals. This extension accommodates, in…
We construct real polarizable Hodge structures on the reduced leafwise cohomology of K\"ahler-Riemann foliations by complex manifolds. As in the classical case one obtains a hard Lefschetz theorem for this cohomology. Serre's K\"ahlerian…
We generalize the theorem of E. Cattani, P. Deligne, and A. Kaplan to admissible variations of mixed Hodge structure.
In this paper we investigate the exactness of the Grassmannian BGG complexes introduced in a previous work (arXiv:1211.2486), and obtain some inequalities between some Hodge numbers of some irregular varieties. In particular, we obtain…
The Hodge algebra structures on the homogeneous coordinate rings of Grassmann varieties provide semi-toric degenerations of these varieties. In this paper we construct these semi-toric degenerations using quasi-valuations and triangulations…
In this paper we complete the proof of Ryba's modular moonshine conjectures. We do this by applying Hodge theory to the cohomology of the monster Lie algebra over the ring of p-adic integers in order to calculate the Tate cohomology groups…
We generalize some results in Hodge theory to generalized normal crossing varieties.