A generalized Hodge theory

Hodge Theory and Lagrangian Planes on Generalized Kummer Fourfolds

Suppose X is a smooth projective complex variety. Let N1(X,Z) ⊂ H2(X,Z) and N(X,Z) ⊂ H(X,Z) denote the group of curve classes modulo homological equivalence and the Néron-Severi group respectively. The monoids of effective classes in each group generate cones NE1(X) ⊂ N1(X,R) and NE(X) ⊂ N(X,R) with closures NE1(X) and NE 1 (X), the pseudoeffective cones. These play a central rôle in the birati...

Hodge Theory and Lagrangian Planes on Generalized Kummer Fourfolds

Suppose X is a smooth projective complex variety. Let N1(X,Z) ⊂ H2(X,Z) and N(X,Z) ⊂ H(X,Z) denote the group of curve classes modulo homological equivalence and the Néron-Severi group respectively. The monoids of effective classes in each group generate cones NE1(X) ⊂ N1(X,R) and NE(X) ⊂ N(X,R) with closures NE1(X) and NE 1 (X), the pseudoeffective cones. These play a central rôle in the birati...

Hodge Theory and Representation Theory

Gauge Theory as Hodge Theory

In the framework of an extended BRST formalism, it is shown that the four (3 + 1)-dimensional (4D) free Abelian 2-form (notoph) gauge theory presents an example of a tractable field theoretical model for the Hodge theory.

Hodge-Tate Theory

This thesis aims to expose the amazing sequence of ideas, concerning p-adic representations coming from geometry, that form the heart of what was called Hodge-Tate theory. This subject, initiated by Tate in the late ’60s in analogy to classical Hodge theory, leads in to the now vast and highly fruitful program of p-adic Hodge Theory. The central result of the theory is the Hodge-Tate decomposit...