Related papers: On localization for cubical higher Chow groups

A tropical version of the Schauder fixed point theorem for compact subsets of tropical linear spaces is proved.

The Beilinson-Bloch type conjectures predict that the low degree rational Chow groups of intersections of quadrics are one dimensional. This conjecture was proved by Otwinowska. Making use of homological projective duality and the recent…

Let $X$ be a cubic hypersurface in $\mathbb P^6$ or a hypersurface of degree greater than equal to $7$ in $\mathbb P^5$. In this note we try to understand, for a very general hyperplane section of $X$, the non-injectivity locus of the…

In this article, we provide a summary of the results presented in the previous two papers of the authors and in the second author's Master thesis, which concern pure cactus groups and configuration spaces of points on the circle.

In this paper, we give an explicit construction of higher Chow cycles of type $(2,1)$ on $K3$ surfaces obtained as quadruple coverings of the projective plane ramified along smooth quartics. The construction uses a pair of bitangents of the…

In this article, we prove a strong relative Novikov conjecture for any pair of groups that are coarsely embeddable into Hilbert space.

In this paper we develop an axiomatic approach to coarse homology theories. We prove a uniqueness result concerning coarse homology theories on the category of `coarse CW-complexes'. This uniqueness result is used to prove a version of the…

We construct a collection of families of higher Chow cycles of type $(2,1)$ on a 2-dimensional family of Kummer surfaces, and prove that for a very general member, they generate a subgroup of rank $\ge 18$ in the indecomposable part of the…

We outline a proof of the categorical geometric Langlands conjecture for GL(2), as formulated in reference [AG], modulo a number of more tractable statements that we call Quasi-Theorems.

We study groups of homeomorphic bijections on spaces that are finite unions of compact connected linearly ordered subsets. We prove that all such groups when endowed with the topology of point-wise convergence are topological groups. }

This note presents a presheaf theoretic approach to the construction of fuzzy sets, which builds on Barr's description of fuzzy sets as sheaves of monomorphisms on a locale. A presheaf-theoretic method is used to show that the category of…

We prove a localization formula for virtual fundamental classes in the context of torus equivariant perfect obstruction theories. As an application, the higher genus Gromov-Witten invariants of projective space are expressed as graph sums…

It is unknown whether smooth cubic threefolds have an (integral Chow-theoretic) decomposition of the diagonal, or whether they are stably rational or not in general. As a first step towards making progress on these questions, we compute the…

In this note we give a generalization for the higher order Hochschild cohomology and show that the secondary Hochschild cohomology is a particular case of this new construction.

The focus of this note is on the Chow group problem over ramified regular local rings $(R, m)$. Our goal is threefold: i) to introduce a characterization of a ramified regular local ring essentially of finite type over a dvr, ii) to address…

We construct a model of the cubic connectedness locus.

We quantize parabolic flag manifolds and describe categories of equivariant quantum $\D$-modules on them at a singular central character. We compute global sections at any $q \in \C^*$ and we also prove a singular version of…

v2: An additional assumption was added in Theorem 4.8. In order to show that a connected abelian group is admissible on the site of locally compact spaces we must in addition assume that it is locally topologically divisible. This condition…

We prove the so called Liv\v{s}ic theorem for cocycles taking values in the group of $C^{1+\beta}-diffeomorphisms of any closed manifold of arbitrary dimension. Since no localization hypothesis is assumed, this result is completely global…

We give a proof of local strong factorization of a birational extension of regular local rings (of equicharacteristic zero) along a valuation of rank 1 and maximal rational rank. This gives an alternate proof to the geometric proof of this…