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Hodge similarities, algebraic classes, and Kuga–Satake varieties
We introduce in this paper the notion of Hodge similarities of transcendental lattices of hyperkähler manifolds and investigate the Hodge conjecture...
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Existence and density of typical Hodge loci
Motivated by a question of Baldi-Klingler-Ullmo, we provide a general sufficient criterion for the existence and analytic density of typical Hodge...
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Hodge theory of degenerations, (I): consequences of the decomposition theorem
We use the Decomposition Theorem to derive several generalizations of the Clemens–Schmid sequence, relating asymptotic Hodge theory of a degeneration...
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Hodge numbers of O’Grady 6 via Ngô strings
We give an alternative computation of the Betti and Hodge numbers for manifolds of OG 6 type using the method of Ngô Strings introduced by de Cataldo,...
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From Grassmann complements to Hodge-duality
Hodge duality is a central concept of 20th century algebraic and analytic geometry and plays a non-negligible role also in recent mathematical...
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FRÖLICHER SPECTRAL SEQUENCE AND HODGE STRUCTURES ON THE COHOMOLOGY OF COMPLEX PARALLELISABLE MANIFOLDS
For complex parallelisable manifolds Γ\ G , with G a solvable or semisimple complex Lie group, the Frölicher spectral sequence degenerates at the...
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Introduction to the Hodge Conjecture for Abelian Varieties
The original version of the conjecture was first formulated by Hodge in his 1950 ICM congress address [64]. In 1961 Atiyah and Hirzebruch formulated...
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The Ax–Schanuel conjecture for variations of mixed Hodge structures
We prove in this paper, the Ax–Schanuel conjecture for all admissible variations of mixed Hodge structures.
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Hodge modules and singular hermitian metrics
The purpose of this paper is to study certain notions of metric positivity called “minimal extension property” for the lowest nonzero piece in the...
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The numerical Hodge standard conjecture for the square of a simple abelian variety of prime dimension
We prove the numerical Hodge standard conjecture for the square of a simple abelian variety of prime dimension, and also in some related cases.
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\(\operatorname {L}^p\) Boundedness of the Hodge Projector
In this chapter, we discuss Łp-boundedness of the Hodge projector associated to L0 (that is, L in the case when a = 1). We obtain a characterization...
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Hodge sheaves underlying flat projective families
We show that, for any fixed weight, there is a natural system of Hodge sheaves, whose Higgs field has no poles, arising from a flat projective family...
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Tame parahoric nonabelian Hodge correspondence in positive characteristic over algebraic curves
Let G be a reductive group, and let X be an algebraic curve over an algebraically closed field k with positive characteristic. We prove a version of...
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The Relative Hodge–Tate Spectral Sequence: An Overview
We give in this note an overview of a recent work (Abbes and Gros, Les suites spectrales de Hodge–Tate. Preprint, 2020....