Related papers: A Proof of the Integral Identity via Braden's Theo…
The integral identity conjecture of Kontsevich and Soibelman plays an important role in proving the existence of motivic Donaldson-Thomas invariants for three-dimensional noncommutative Calabi-Yau manifolds. There are a number of different…
It is well known that the integral identity conjecture is of prime importance in Kontsevich-Soibelman's theory of motivic Donaldson-Thomas invariants for non-commutative Calabi-Yau threfolds. In this article we consider its numerical…
We define metric bundles/metric graph bundles which provide a purely topological/coarse-geometric generalization of the notion of trees of metric spaces a la Bestvina-Feighn in the special case that the inclusions of the edge spaces into…
We study the motive of the moduli space of semistable Higgs bundles of coprime rank and degree on a smooth projective curve C over a field k under the assumption that C has a rational point. We show this motive is contained in the thick…
We prove in this paper the original version of Kontsevich and Soibelman's motivic integral identity conjecture for formal functions by developing a novel framework for equivariant motivic integration on special rigid varieties. This theory…
We prove a motivic integral identity relating the motivic Behrend function of a $(-1)$-shifted symplectic stack to that of its stack of graded points. This generalizes analogous identities for moduli stacks of objects in…
We define and study the motive of the moduli stack of vector bundles of fixed rank and degree over a smooth projective curve in Voevodsky's category of motives. We prove that this motive can be written as a homotopy colimit of motives of…
This article develops a unified and intrinsic framework for the theory of Sobolev spaces on vector bundles over Riemannian manifolds. The analytical core of our approach is an explicit higher-order geometric integration by parts formula,…
In this article, we give a construction of the (un-)stable motivic homotopy category of an algebraic stack in the spirit of Morel-Voevodsky. We prove that this new construction agrees with the stable motivic homotopy category defined by…
This paper is part of the general project of proof mining, developed by Kohlenbach. By "proof mining" we mean the logical analysis of mathematical proofs with the aim of extracting new numerically relevant information hidden in the proofs.…
An algebraic version of a theorem due to Quillen is proved. More precisely, for a ground field k we consider the motivic stable homotopy category SH(k) of P^1-spectra equipped with the symmetric monoidal structure described in…
We prove a new convergence result for the slice spectral sequence, following work by Levine and Voevodsky. This verifies a derived variant of Voevodsky's conjecture on convergence of the slice spectral sequence. This is, in turn, a…
We prove the version of Joyce-Song formula for the Behrend function identities in the motivic setting. The main method we use is the proof of Kontsevich-Soibelman conjecture about the motivic Milnor fibers by Q. T. Le, who uses the method…
Aiming to provide weak as possible axiomatic assumptions in which one can develop basic linear algebra, we give a uniform and integral version of the short propositional proofs for the determinant identities demonstrated over $GF(2)$ in…
For any base field and integer $l$ invertible in $k$, we prove that $\Omega^\infty_{\mathbb{G}_m}$ and $\Omega^\infty_{\mathbb{P}^1}$ commute with hyper \'etale sheafification $L_{\acute{e}t}$ and Betti realization through infinite loop…
We give a new proof of Braden's theorem ([Br]) about \emph{hyperbolic restrictions} of constructible sheaves/D-modules. The main geometric ingredient in the proof is a 1-parameter family that degenerates a given scheme Z equipped with a…
In this note, using Cluckers-Loeser's theory of motivic integration, we prove the integral identity conjecture with framework a localized Grothendieck ring of varieties over an arbitrary base field of characteristic zero.
With representation-theoretic applications in mind, we construct a formalism of reduced motives with integral coefficients. These are motivic sheaves from which the higher motivic cohomology of the base scheme has been removed. We show that…
We formulate and establish a generalization of Koll\'ar's injectivity theorem for adjoint bundles twisted by suitable multiplier ideal sheaves. As applications, we generalize Koll\'ar's torsion-freeness, Koll\'ar's vanishing theorem, and a…
Recently, it is well known that the conjectural integral identity is of crucial importance in the motivic Donaldson-Thomas invariants theory for non-commutative Calabi-Yau threefolds. The purpose of this article is to consider different…