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...

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...

now called Hodge theory and pertaining more generally to Kähler manifolds—has been a major influence on subsequent work in geometry. Hodge was born in...

In mathematics, p-adic Hodge theory is a theory that provides a way to classify and study p-adic Galois representations of characteristic 0 local fields...

In mathematics, the Hodge conjecture is a major unsolved problem in algebraic geometry and complex geometry that relates the algebraic topology of a non-singular...

In mathematics, Hodge–Arakelov theory of elliptic curves is an analogue of classical and p-adic Hodge theory for elliptic curves carried out in the framework...

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

{\displaystyle 2p} , and in the direct sum decomposition of H shown to exist in Hodge theory, x is purely of type ( p , p ) {\displaystyle (p,p)} . Secondly, x is...

The Laplacian is the simplest elliptic operator and is at the core of Hodge theory as well as the results of de Rham cohomology. The Laplace operator is...

functional equations of L-functions. Deligne also focused on topics in Hodge theory. He introduced the concept of weights and tested them on objects in complex...

theory Hodge theory Homology theory Homotopy theory Ideal theory Index theory Information theory Intersection theory Invariant theory Iwasawa theory K-theory...

In mathematics, the Hodge star operator or Hodge star is a linear map defined on the exterior algebra of a finite-dimensional oriented vector space endowed...

theory — Galois theory — Game theory — Gauge theory — Graph theory — Group theory — Hodge theory — Homology theory — Homotopy theory — Ideal theory —...

2019) was a French mathematician. He was one of the founders of p-adic Hodge theory. He was a professor at Paris-Sud 11 University from 1988 to his death...

appropriate definition of harmonic forms and of the Hodge theorem. For further details see Hodge theory. If M is a compact Riemannian manifold, then each...

It is a generalization of a Hodge structure, which is used to study smooth projective varieties. In mixed Hodge theory, where the decomposition of a...

advisor was Phillip A. Griffiths. His dissertation thesis was titled Hodge Theory and the Local Torelli Problem. He is currently a professor of mathematics...

In algebraic geometry and the theory of complex manifolds, a logarithmic differential form is a differential form with poles of a certain kind. The concept...

m}\right)\right].} Hodge–Arakelov theory Hodge theory P-adic Hodge theory Adelic group Leong, Y. K. (July–December 2018). "Shou-Wu Zhang: Number Theory and Arithmetic...

During the war years he worked in isolation, but was able to master Hodge theory as it then stood. He obtained his PhD from the University of Tokyo in...

group G is said to be of Hodge–Tate type if it is generated by the eigenvectors of integral powers of χ. p-adic Hodge theory Mumford–Tate group Faltings...

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

such as Hodge theory of Kähler manifolds inspire understanding of Hodge structures for varieties and schemes as well as p-adic Hodge theory, deformation...

Edwin Martel Basil Hodge (born January 26, 1985) is an American actor. He is recognized for portraying Dante Bishop in The Purge film series, and is the...

spaces of vector bundles, higher non-abelian de Rham cohomology (Hodge theory), the theory of higher categories and computer verification of mathematical...

Kähler geometry, and Hodge theory. Over non-complex manifolds, they also play a role in the study of almost complex structures, the theory of spinors, and...

Mochizuki has also worked in Hodge–Arakelov theory and p-adic Teichmüller theory. Mochizuki developed inter-universal Teichmüller theory, which has attracted...

foundations of algebraic geometry to include, for example, techniques from Hodge theory. (NB While analytic geometry as use of Cartesian coordinates is also...

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

1974, pp. 389. Peano 1889, p. 1. Peano 1908, p. 27. Halmos 1974, p. 32. Hodges 2009, p. 14. Hext 1990. Graham, Knuth & Patashnik 1994, p. 381. Blokhintsev...