mathematics, a Hodge structure, named after W. V. D. Hodge, is an algebraic structure at the level of linear algebra, similar to the one that Hodge theory gives...

In algebraic geometry, a mixed Hodge structure is an algebraic structure containing information about the cohomology of general algebraic varieties. It...

Vallance Douglas Hodge as a result of a work in between 1930 and 1940 to enrich the description of de Rham cohomology to include extra structure that is present...

In mathematics, Hodge theory, named after W. V. D. Hodge, is a method for studying the cohomology groups of a smooth manifold M using partial differential...

In mathematics, mixed Hodge modules are the culmination of Hodge theory, mixed Hodge structures, intersection cohomology, and the decomposition theorem...

mathematics, a Hodge–Tate module is an analogue of a Hodge structure over p-adic fields. Serre (1967) introduced and named Hodge–Tate structures using the...

metrics. Every smooth complex projective variety is a Kähler manifold. Hodge theory is a central part of algebraic geometry, proved using Kähler metrics...

Sir William Vallance Douglas Hodge FRS FRSE (/hɒdʒ/; 17 June 1903 – 7 July 1975) was a British mathematician, specifically a geometer. His discovery of...

In algebraic geometry and differential geometry, the nonabelian Hodge correspondence or Corlette–Simpson correspondence (named after Kevin Corlette and...

related Hodge-theoretic concepts. This idea has applications in the theory of moduli spaces, in deformation theory and Fontaine's p-adic Hodge theory,...

using a variation of Hodge structure on the moduli of algebraic K3 surfaces to show that all such K3 surfaces have the same Hodge numbers. A more low-brow...

This is shown using the Kodaira–Spencer map. In Hodge theory, there are objects called real Hodge structures which are the data of a real vector space H R...

algebraic geometry, the Mumford–Tate group (or Hodge group) MT(F) constructed from a Hodge structure F is a certain algebraic group G. When F is given...

diamond Hodge duality Hodge filtration Hodge index theorem Hodge group Hodge star operator Hodge structure Mixed Hodge structure Hodge–Tate module Hodge theory...

relations between Hodge structure and l-adic representation. Morally, the philosophy of motives tells us that the Hodge structure and the Galois representation...

named the Hodge Building in memory of Colonel William Walter Hodge, commander of the 93rd Engineer Regiment on the Alcan Highway. The Hodge Building was...

its Hodge structure is a full functor H : M ( k ) Q → H S Q {\displaystyle H:M(k)_{\mathbb {Q} }\to HS_{\mathbb {Q} }} (rational Hodge structures). Here...

a major developer in particular of the theory of variation of Hodge structure in Hodge theory and moduli theory, which forms part of transcendental algebraic...

Hodge conjecture, for some applications. The theory of mixed Hodge structures, a powerful tool in algebraic geometry that generalizes classical Hodge...

embeds into the cohomology of a torus, in a way that preserves the Hodge structure. This can be easily seen by noting that Sp(n) is a subgroup of the...

family (V, ρ ⋅ h) is a holomorphic family of Hodge structures; moreover, it forms a variation of Hodge structure, and X is a finite disjoint union of hermitian...

matrices are a useful technique for computing the Jacobian of a curve Hodge structure – these are generalizations of Jacobians Honda–Tate theorem – classifies...

family of varieties (encoded as period integrals on a variation of Hodge structures). In short, this means there is a relation between the number of genus...

period mapping relates families of Kähler manifolds to families of Hodge structures. Let f : X → B be a holomorphic submersive morphism. For a point b...

of Hodge structures and mirror symmetry, and has written several books on Hodge theory. In 2002, Voisin proved that the generalization of the Hodge conjecture...

formula Borel–Moore homology Differential of the first kind Log structure Mixed Hodge structure Residue theorem Poincaré residue Deligne (1970), section II...

Bundle gerbe Motivic cohomology Hodge structure Intermediate Jacobian Hopkins, Michael J.; Quick, Gereon (March 2015). "Hodge filtered complex bordism". Journal...

= E ∞ {\displaystyle E_{1}=E_{\infty }} . This gives the canonical Hodge structure on the cohomology groups H k ( X , C ) {\displaystyle H^{k}(X,\mathbb...

University of Amsterdam with thesis advisor Frans Oort and thesis Limits of Hodge Structures and Intermediate Jacobians. He is now a professor at Radboud University...

semisimple. An example from Hodge theory is the category of polarizable pure Hodge structures, i.e., pure Hodge structures equipped with a suitable positive...