Related papers: Exponential map in DT theory
We prove the multiplicative version of the dimensional reduction theorem in cohomological Donaldson--Thomas theory. More precisely, we show that the BPS cohomology associated with the loop stack of a $0$-shifted symplectic stack admits a…
This review gives an introduction to cohomological Donaldson-Thomas theory: the study of a cohomology theory on moduli spaces of sheaves on Calabi-Yau threefolds, and of complexes in 3-Calabi-Yau categories, categorifying their numerical DT…
In this paper we prove a toric localization formula in the cohomological Donaldson-Thomas theory. Consider a (-1)-shifted symplectic algebraic space with a $\mathbb{G}_m$-action leaving the (-1)-shifted symplectic form invariant (typical…
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…
In this paper we prove a toric localization formula in cohomological Donaldson Thomas theory. Consider a -1-shifted symplectic algebraic space with a C* action leaving the -1-shifted symplectic form invariant. This includes the moduli space…
We show the existence of semiorthogonal decompositions of Donaldson-Thomas categories for $(-1)$-shifted cotangent derived stacks associated with $\Theta$-stratifications on them. Our main result gives an analogue of window theorem for…
We define a new type of Hall algebras associated e.g. with quivers with polynomial potentials. The main difference with the conventional definition is that we use cohomology of the stack of representations instead of constructible sheaves…
This is the first paper in a series on intrinsic Donaldson-Thomas theory, where we develop a new framework for enumerative geometry that allows the generalization of constructions and results from linear moduli stacks to general non-linear…
For oriented $-1$-shifted symplectic derived Artin stacks, Ben-Bassat-Brav-Bussi-Joyce introduced certain perverse sheaves on them which can be regarded as sheaf theoretic categorifications of the Donaldson-Thomas invariants. In this paper,…
This is the second paper in a series on intrinsic Donaldson-Thomas theory, a framework for studying the enumerative geometry of general algebraic stacks. In this paper, we present the construction of Donaldson-Thomas invariants for general…
In this paper, we prove the integrality conjecture for quotient stacks arising from weakly symmetric representations of reductive groups. Our main result is a decomposition of the cohomology of the stack into finite-dimensional components…
We prove that the mapping stack Map(Y,X) of topological stacks X and Y is again a topological stack if Y admits a compact groupoid presentation. If Y admits a locally compact groupoid presentation, we show that Map(Y,X) is a paratopological…
We introduce volume forms on mapping stacks in derived algebraic geometry using a parametrized version of the Reidemeister-Turaev torsion. In the case of derived loop stacks we describe this volume form in terms of the Todd class. In the…
We introduce a derived enhancement of the moduli space of sections defined by Chang-Li, and we compute its tangent complex. Special cases of this moduli space include stable maps and stable quasi-maps. As an application, we prove that…
In this note, we give a formulation of log structures for derived stacks using Olsson's log stack. The derived cotangent complex is then Olsson's logarithmic cotangent complex, which (unlike Gabber's) is just given by log differential forms…
We construct and study Donaldson-Thomas invariants counting orthogonal and symplectic objects in linear categories, which are a generalization of the usual Donaldson-Thomas invariants from the structure groups $\mathrm{GL} (n)$ to the…
The present paper is an extension of a previous paper written in collaboration with Markus Reineke dealing with quiver representations. The aim of the paper is to generalize the theory and to provide a comprehensive theory of…
We establish a system of formal noncommutative calculus for differential forms and polyvector fields, which forms the foundations for the study of pre-Calabi-Yau categories. Using an explicit trace map, we show that any $n$-Calabi-Yau…
This is the first of a series of papers about \emph{quantization} in the context of \emph{derived algebraic geometry}. In this first part, we introduce the notion of \emph{$n$-shifted symplectic structures}, a generalization of the notion…
We develop a characterisation of non-Archimedean derived analytic geometry based on dg enhancements of dagger algebras. This allows us to formulate derived analytic moduli functors for many types of pro-\'etale sheaves, and to construct…