The ‘Folk Theorem’ that a smooth action by a compact Lie group can be (canonically) resolved, by iterated blow up, to have unique isotropy type is proved in the context of manifolds with corners. This procedure is shown to capture the simultaneous resolution of all isotropy types in a ‘resolution tower’ which projects to a resolution, with iterated boundary fibration, of the quotient. Equivaria...

Following Feigin and Fuchs, we compute the first cohomology of Lie superalgebra $\mathcal{K}(1)$ contact vector fields on (1,1)-dimensional real superspace with coefficients in linear differential operators acting superspaces weighted densities. We also same, but $\mathfrak{osp}(1|2)$-relative, cohomology. explicitly give 1-cocycles spanning these classify generic formal $\mathfrak{osp}(1|2)$-t...

We generalize Macdonald’s formula for the cohomology of Hilbert schemes of points on a curve from smooth curves to curves with planar singularities: we relate the cohomology of the Hilbert schemes to the cohomology of the compactified Jacobian of the curve. The new formula is a consequence of a stronger identity between certain perverse sheaves defined by a family of curves satisfying mild cond...

We prove that for any field k of characteristic p > 0, any separated scheme X of finite type over k, and any overconvergent F -isocrystal E over X, the rigid cohomology H i rig(X, E) and rigid cohomology with compact supports H i c,rig(X, E) are finite dimensional vector spaces over an appropriate p-adic field. We also establish Poincaré duality and the Künneth formula with coefficients. The ar...

A refined form of the ‘Folk Theorem’ that a smooth action by a compact Lie group can be (canonically) resolved, by iterated blow up, to have unique isotropy type was established in [1] in the context of manifolds with corners; the canonical construction induces fibrations on the boundary faces of the resolution resulting in an ‘equivariant resolution structure’. Here, equivariant K-theory and t...

We describe representations of certain superconformal algebras in the semi-infinite Weil complex related to the loop algebra of a complex finite-dimensional Lie algebra and in the semi-infinite cohomology. We show that in the case where the Lie algebra is endowed with a nondegenerate invariant symmetric bilinear form, the relative semi-infinite cohomology of the loop algebra has a structure, wh...

In this paper, we consider a class of connected oriented (with respect to Z/p) closed G-manifolds with a non-empty finite fixed point set, each of which is G-equivariantly formal, where G = Z/p and p is an odd prime. Using localization theorem and equivariant index, we give an explicit description of the mod p equivariant cohomology ring of such a G-manifold in terms of algebra. This makes ...

We study modular subspaces corresponding to two deformation functors associated to an isolated singularity X0: the functor DefX0 of deformations of X0 and the functor Def X0 of deformations with section of X0. After recalling some standard facts on the cotangent cohomology of analytic algebras and the general theory of deformations with section, we give several criteria for modularity in terms ...

Displays were introduced to classify formal p-divisible groups over an arbitrary ring R where p is nilpotent. We define a more general notion of display and obtain an exact tensor category. In many examples the crystalline cohomology of a smooth and proper scheme X over R carries a natural display structure. It is constructed from the relative de Rham-Witt complex. For this we refine the compar...

In this paper, we investigate analytical and geometric properties of certain non-compact boundary-manifolds, namely manifolds of bounded geometry. One result are strong Bochner type vanishing results for the L-cohomology of these manifolds: if e.g. a manifold admits a metric of bounded geometry which outside a compact set has nonnegative Ricci curvature and nonnegative mean curvature (of the bo...