Mumford-Tate groups of mixed Hodge structures and the theorem of the fixed part

The theory of variation of Hodge Structure (VHS) adds to the local system the Hodge structures on the cohomology of the fibers, and transforms geometric prob- lems concerning

The above exact sequence then gives the prime-to-p part of the main theorem of unramified class field theory for surfaces over a finite field (studied by Parshin, Bloch,

We use mixed Hodge theory to show that the functor of singular chains with rational coefficients is formal as a lax symmetric monoidal functor, when restricted to complex

With each such a we associate the braid which is the union of the strings of β starting at a and the strings obtained by shrinking the tubes corresponding to the interior components

In Section 4, by using the theory of p-adic differential modules, we shall prove the main theorem, first for Hodge-Tate representations and then for de Rham

Galois representations and associated operators By a (linear) Galois representation ^ we mean a continuous homo- morphism ^ : Q —>• 7?.* where 7^* is the group of units of a

for elliptic curves E defined over function fields provided the Tate-Shafarevich group for the function field is finite.. This provides an effective algorithm

The main result, whose proof uses the purity of the intersection complex in terms of mixed Hodge modules, is a generalization of the semipurity theorem obtained by