Related papers: On localization for cubical higher Chow groups

We introduce new foundations for relative topos theory based on stacks. One of the central results in our theory is an adjunction between the category of toposes over the topos of sheaves on a given site $({\mathcal{C}}, J)$ and that of…

We show a classification method for finite groupoids and discuss the cardinality of cosets and its relation with the index. We prove a generalization of the Lagrange's Theorem and establish a Sylow theory for groupoids.

We prove a formula for Chow groups of $Quot$-schemes which resolve degeneracy loci of a map between vector bundles, under expected dimension conditions. This result provides a unified way to understand known formulae for various geometric…

We introduce some classical concepts in the representation theory of compact groups, in order to use them for a new generalization of the Peter-Weyl Theorem. We mostly deal with functions on locally compact groups possessing large…

We study Lefschetz fixed point formulas for constructible sheaves with higher-dimensional fixed point sets. Under fairly weak assumptions, we prove that the local contributions from them are expressed by some constructible functions…

We construct nontrivial homomorphisms from the quasi group of some cubic surfaces over $\bbF_{\!p}$ into a group. We show experimentally that the homomorphisms constructed are the only possible ones and that there are no nontrivial…

We study locally compact contractive local groups, that is, locally compact local groups with a contractive pseudo-automorphism. We prove that if such an object is locally connected, then it is locally isomorphic to a Lie group. We also…

The Linearization Theorem for proper Lie groupoids organizes and generalizes several results for classic geometries. Despite the various approaches and recent works on the subject, the problem of understanding invariant linearization…

The paper provides a computation of the equivariant Chow group of a rational, complete, complexity one $T$-variety

We introduce some general and special formulations of general position theorem for parametrized families of fractals and explain the techniques of its application to prove the existence of self-similar sets with prescribed special…

We propose a localization formula for the chiral de Rham complex generalizing the well-known localization procedure in topological theories. Our formula takes into account the contribution due to the massive modes. The key to achieve this…

We use double categories to obtain a single theorem characterizing certain exponentiable morphisms of small categories, topological spaces, locales, and posets.

We prove the even isomorphism theorem for Coxeter groups

We fill a lacuna in the literature by giving a version in dimension 1 of the Relative Hurewicz Theorem, and relate this to abelianisations of groupoids, covering spaces and covering morphisms of groupoids, and Crowell's notion of derived…

We prove the equivalence of several hypotheses that have appeared recently in the literature for studying left Bousfield localization and algebras over a monad. We find conditions so that there is a model structure for local algebras, so…

We give an different proof of our result computing the stable homology of dihedral group Hurwitz spaces. This proof employs more elementary methods, instead of higher algebra.

We characterize group compactifications of discrete groups for which there exists an equivariant retraction onto the boundary. In particular, we prove an equivariant analogue of Brouwer's No-Retraction theorem for large classes of group…

Every locally compact local group is locally isomorphic to a topological group.

The survey presents the main developments obtained over the last decade regarding pointwise ergodic theorems for measure preserving actions of locally compact groups. The survey includes an exposition of the solutions to a number of long…

We develop a motivic cohomology theory, representable in the Voevodsky's triangulated category of motives, for smooth separated Deligne-Mumford stacks and show that the resulting higher Chow groups are canonically isomorphic to the higher…