• Corpus ID: 46908692


  author={Bertrand To{\"e}n},
– The purpose of this work is to prove the existence of an algebraic moduli classifying objects in a given triangulated category. To any dg-category T (over some base ring k), we define a D−-stack MT in the sense of [TOËN B., VEZZOSI G., Homotopical algebraic geometry II: Geometric stacks and applications, Mem. Amer. Math. Soc., in press], classifying certain T -dg-modules. When T is saturated, MT classifies compact objects in the triangulated category [T ] associated to T . The main result of… 
Categorical formal punctured neighborhood of infinity, I
In this paper we introduce and study the formal punctured neighborhood of infinity, both in the algebro-geometric and in the DG categorical frameworks. For a smooth algebraic variety $X$ over a field
$\mathbb{A}^{1}$ -homotopy invariants of topological Fukaya categories of surfaces
We provide an explicit formula for localizing $\mathbb{A}^{1}$ -homotopy invariants of topological Fukaya categories of marked surfaces. Following a proposal of Kontsevich, this differential
Non-commutative virtual structure sheaves
The moduli spaces of stable sheaves on projective schemes admit certain gluing data of Kapranov's NC structures, which we call quasi NC structures. The formal completion of the quasi NC structure at
Motives of Noncommutative Tori
In this article, we propose a way of seeing the noncommutative tori in the category of noncommutative motives. As an algebra, the noncommutative torus is lack the smoothness property required to
Motivic structures in non-commutative geometry
We review some recent results and conjectures saying that, roughly speaking, periodic cyclic homology of a smooth non-commutative algebraic variety should carry all the additional "motivic"
A Riemann-Roch Theorem for dg Algebras
Given a smooth proper dg-algebra $A$, a perfect dg $A$-module $M$, and an endomorphism $f$ of $M$, we define the Hochschild class of the pair $(M,f)$ with values in the Hochschild homology of $A$.
Trace formula for dg-categories and Bloch's conductor conjecture I
We present an $\ell$-adic trace formula for saturated and admissible dg-categories over a base monoidal dg-category. As an application, we prove (a version of) Bloch's conductor conjecture, under the
A remark on the Hochschild-Kostant-Rosenberg theorem in characteristic p
We prove a Hochschild-Kostant-Rosenberg decomposition theorem for smooth proper schemes $X$ in characteristic $p$ when $\dim X\leq p$. The best known previous result of this kind, due to Yekutieli,


Homotopical algebraic geometry. I. Topos theory.
Injective resolutions of BG and derived moduli spaces of local systems
The homotopy theory of dg-categories and derived Morita theory
The main purpose of this work is to study the homotopy theory of dg-categories up to quasi-equivalences. Our main result is a description of the mapping spaces between two dg-categories C and D in
Configurations in abelian categories. II. Ringel–Hall algebras
A holomorphic Casson invariant for Calabi-Yau 3-folds, and bundles on K3 fibrations
We briefly review the formal picture in which a Calabi-Yau n-fold is the complex analogue of an oriented real n-manifold, and a Fano with a fixed smooth anticanonical divisor is the analogue of a
Moduli of complexes on a proper morphism
Given a proper morphism X -> S, we show that a large class of objects in the derived category of X naturally form an Artin stack locally of finite presentation over S. This class includes S-flat
Derived Hilbert schemes
We construct the derived version of the Hilbert scheme parametrizing subschemes in a given projective scheme X with given Hilbert polynomial h. This is a dg-manifold (smooth dg-scheme) RHilb_h(X)
Monoidal model categories
A monoidal model category is a model category with a compatible closed monoidal structure. Such things abound in nature; simplicial sets and chain complexes of abelian groups are examples. Given a
Equivalences of monoidal model categories
We construct Quillen equivalences between the model categories of monoids (rings), modules and algebras over two Quillen equivalent model categories under certain conditions. This is a continuation
Algebras and Modules in Monoidal Model Categories
In recent years the theory of structured ring spectra (formerly known as A∞‐ and E∞‐ring spectra) has been simplified by the discovery of categories of spectra with strictly associative and