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Suwa investigated the unit group scheme of the group ring associated with a finite flat group scheme and provided a characterization of torsors possessing the normal base property for such schemes. In this paper, we examine the unit group…

Let $\Gamma$ be a finite-index subgroup of the mapping class group of a closed genus $g$ surface that contains the Torelli group. For instance, $\Gamma$ can be the level $L$ subgroup or the spin mapping class group. We show that…

This article studies left-invariant Hermitian structures on Lie groups with two-dimensional commutator subgroups. We provide an explicit classification for two specific types of such structures, which we designate as Type I and Type II.…

We describe the structure of the top tautological group in the cohomology of the moduli space of smooth genus $g$ curves with $n$ marked points.

We introduce an exact category of torsion-free constructible tori and an abelian category of constructible tori over a Dedekind scheme with perfect residue fields. The first one has an explicit description as $2$-term complexes of smooth…

The aim of this paper is to explain how to get a complex of smooth representations out of the dual vector space to a smooth representation of a p-adic Lie group, in natural characteristic. The construction does not depend on any…

A duality theorem for the stable module category of representations of a finite group scheme is proved. One of its consequences is an analogue of Serre duality, and the existence of Auslander-Reiten triangles for the $\mathfrak{p}$-local…

This paper is a sequel to "Localization of $\frak{u}$-modules. I", hep-th/9411050. We are starting here the geometric study of the tensor category $\cal{C}$ associated with a quantum group (corresponding to a Cartan matrix of finite type)…

The homology of Kontsevich's commutative graph complex parameterizes finite type invariants of odd dimensional manifolds. This {\it graph homology} is also the twisted homology of Outer Space modulo its boundary, so gives a nice point of…

In this paper we will study the Hessian hypersurface associated with a smooth cubic. We prove that the existence of a Hessian locus, associated with a smooth cubic form f, of dimension bigger then the expected one, forces the cubic f to be…

We study the descent behaviour of homotopy-theoretic properties of smooth complex affine surfaces under finite surjective morphisms. We first examine the Eilenberg-MacLane property and show, by means of an explicit counterexample, that it…

In this note, we extend the theory of Chern-Cheeger-Simons to construct canonical invariants for a one-parameter family of flat connections on a smooth manifold. These invariants lie in degrees $(2p-2)$-cohomology with $\C/\Z$-cohomology,…

In this work we relate the known results about the homotopy type of classifying spaces for smooth foliations, with the homology and cohomology of the discrete group of diffeomorphisms of a smooth compact connected oriented manifold. The…

We explain the relationship between various characteristic classes for smooth manifold bundles known as ``higher torsion'' classes. We isolate two fundamental properties that these cohomology classes may or may not have: additivity and…

A general structure theorem on higher order invariants is proven. For an arithmetic group, the structure of the corresponding Hecke module is determined. It is shown that the module does not contain any irreducible submodule. This explains…

For a smooth projective variety $X$ over a number field $k$ a conjecture of Bloch and Beilinson predicts that the kernel of the Albanese map of $X$ is a torsion group. In this article we consider a product $X=C_1\times\cdots\times C_d$ of…

For a compact complex manifold, we introduce holomorphic foliations associated with certain abelian subgroups of the automorphism group. Such foliations are generalizations of holomorphic principal torus bundles. If there exists a…

Let $R$ be a discrete valuation ring of field of fractions $K$ and of residue field $k$ of characteristic $p > 0$. In an earlier work, we studied the question of extending torsors on $K$-curves into torsors over $R$-regular models of the…

In the present paper we study abelian extensions of connected Lie groups $G$ modeled on locally convex spaces by smooth $G$-modules $A$. We parametrize the extension classes by a suitable cohomology group $H^2_s(G,A)$ defined by locally…

We prove the vanishing modulo torsion of the higher direct images of the sheaf of Witt vectors (and the Witt canonical sheaf) for a purely inseparable projective alteration between normal finite quotients over a perfect field. For this, we…