Annette Huber

The slice filtration and mixed Tate motives

Using the ‘slice filtration’, defined by effectivity conditions on Voevodskys triangulated motives, we define spectral sequences converging to their motivic cohomology and etale motivic cohomology. These spectral sequences are particularly interesting in the case of mixed Tate motives as their

Mixed motives and their realization in derived categories

E_2

Bloch-Kato conjecture and main conjecture of Iwasawa theory for Dirichlet characters

-terms then have a simple description. In particular this yields spectral sequences converging to the motivic cohomology of a split connected reductive group. We also describe in detail the multiplicative structure of the motive of a split torus.

Mixed perverse sheaves for schemes over number fields

Basic notions.- Derived categories of exact categories.- Filtered derived categories.- Gluing of categories.- Godement resolutions.- Singular cohomology.- De Rham cohomology.- Hodge realization.- 1-adic cohomology.- Comparison functors: 1-adic versus singular realization.- The mixed realization.- The tate twist.- ?-product and internal hom on D MR .- The Kunneth morphism.- The Bloch-Ogus axioms.- The Chern class of a line bundle.- Classifying spaces.- Higher Chern classes.- Operations of correspondences.- Grothendieck motives.- Polarizability.- Mixed motives.

Calculation of derived functors via Ind-categories

This is the completely revised version of math.AG/0101071.

Differential forms in the h-topology

This paper generalizes the definition of mixed perverse sheavesto schemes of finite type over a number field.Their basic properties, e.g., characterization of simple objects, are shown.

Dirichlet motives via modular curves

Abstract We show that in nice cases it is possible to calculate the cohomological derived functor by using injective resolutions in the Ind-category.

A p-adic analogue of the Borel regulator and the Bloch-Kato exponential map

We study sheaves of differential forms and their cohomology in the h-topology. This allows to extend standard results from the case of smooth varieties to the general case. As a first application we explain the case of singularities arising in the Minimal Model Program. As a second application we consider de Rham cohomology.

A cohomological Tamagawa number formula

Abstract Generalizing ideas of Anderson, Harder has proposed a construction of extensions of Tate-motives (more precisely of Hodge structures and Galois modules, respectively) in terms of modular curves. The aim of this paper is to construct directly those elements of motivic cohomology of Spec Q (μN) (i.e. in K∗(Spec Q (μN))) which induce these extensions in absolute Hodge cohomology and continuous Galois cohomology. We give two such constructions and prove that they are equivalent. The key ingredient is Beilinsons Eisenstein symbol in motivic cohomology of powers of the universal elliptic curve over the modular curve. We also compute explicitly the Harder-Anderson element in absolute Hodge cohomology. It is given in terms of Dirichlet-L-functions. As a corollary, we get a new proof of Beilinsons conjecture for Dirichlet-L-functions. A second paper [HuK] treats the explicit computation in the l-adic case.

Polylogarithm for families of commutative group schemes

In this paper we define a p-adic analogue of the Borel regulator for the K-theory of p-adic fields. The van Est isomorphism in the construction of the classical Borel regulator is replaced by the Lazard isomorphism. The main result relates this p-adic regulator to the BlochKato exponential and the Soule regulator. On the way we give a new description of the Lazard isomorphism for certain formal groups.