Hodge Representations

G-VALUED CRYSTALLINE REPRESENTATIONS WITH MINUSCULE p-ADIC HODGE TYPE

We study G-valued semi-stable Galois deformation rings where G is a reductive group. We develop a theory of Kisin modules with G-structure and use this to identify the connected components of crystalline deformation rings of minuscule p-adic Hodge type with the connected components of moduli of “finite flat models with G-structure.” The main ingredients are a construction in integral p-adic Hod...

Hodge Groups of Hodge Structures with Hodge Numbers

This paper studies the possible Hodge groups of simple polarizable Q-Hodge structures with Hodge numbers (n, 0, . . . , 0, n). In particular, it generalizes earlier work of Ribet and MoonenZarhin to completely determine the possible Hodge groups of such Hodge structures when n is equal to 1, 4, or a prime p. In addition, the paper determines possible Hodge groups, under certain conditions on th...

Hodge loci and absolute Hodge classes

Hidden Hodge symmetries and Hodge correlators

l-adic Étale Theory Hodge Theory Category of l-adic Abelian category MHR Galois modules of real mixed Hodge strucrures Galois group Hodge Galois group GHod := Gal(Q/Q) Galois group of the category MHR Gal(Q/Q) acts on H∗ et(X,Ql), H∗(X(C),R) has a functorial where X is a variety over Q real mixed Hodge structure étale site ?? Gal(Q/Q) acts on the étale site, and thus ?? on categories of étale s...

On the Hodge Filtration of Hodge Modules

Let X be a complex manifold, and Z an irreducible closed analytic subset. We have the polarizable Hodge Module ICZQ H whose underlying perverse sheaf is the intersection complex ICZQ. See [16]. Let (M,F ) be its underlying filtered DX -Module. ThenM is the unique regular holonomic DX -Module which corresponds to ICZC by the Riemann-Hilbert correspondence [9] [13], and it is relatively easy to d...