Related papers: Derived log stacks after Olsson

A moduli space of stable quotients of the rank n trivial sheaf on stable curves is introduced. Over nonsingular curves, the moduli space is Grothendieck's Quot scheme. Over nodal curves, a relative construction is made to keep the torsion…

We develop a theory of good moduli spaces for derived Artin stacks, which naturally generalizes the classical theory of good moduli spaces introduced by Alper. As such, many of the fundamental results and properties regarding good moduli…

We construct the derived scheme of stable sheaves on a smooth projective variety via derived moduli of finite graded modules over a graded ring. We do this by dividing the derived scheme of actions of Ciocan-Fontanine and Kapranov by a…

We introduce a formalism for derived moduli functors on differential graded associative algebras, which leads to non-commutative enhancements of derived moduli stacks and naturally gives rise to structures such as Hall algebras. Descent…

We show how a quasi-smooth derived enhancement of a Deligne-Mumford stack X naturally endows X with a functorial perfect obstruction theory in the sense of Behrend-Fantechi. This result is then applied to moduli of maps and perfect…

A theory of dg schemes is developed so that it becomes a homotopy site, and the corresponding infinity category of stacks is equivalent to the infinity category of stacks, as constructed by Toen and Vezzosi, on the site of dg algebras whose…

Given a derived equivalence of orbifolds associated to projective varieties with (not necessarily Gorenstein) quotient singularities, we deduce consequences related to the behavior of orbifold Hodge numbers and the Picard variety, extending…

Stacks have become a prevalent tool in studying problems with connections to String Theory, hence we see a need to develop a theory of supersymmetric stacks proper. We first define derived stacks on $\mathbb{Z}_2$-bi-graded k-modules…

We survey several recent examples of derived structures emerging in connection with the Langlands correspondence. Cases studies include derived Galois deformation rings, derived Hecke algebras, derived Hitchin stacks, and derived special…

Given a graded vector space V, the variety of complexes Com(V) consists of all differentials making V into a cochain complex. This variety was first introduced by Buchsbaum and Eisenbud and later studied by Kempf, De Concini, Strickland and…

This note extends some recent results on the derived category of a geometric invariant theory quotient to the setting of derived algebraic geometry. Our main result is a structure theorem for the derived category of a derived local quotient…

We introduce and study the derived moduli stack $\mathrm{Symp}(X,n)$ of $n$-shifted symplectic structures on a given derived stack $X$, as introduced by [PTVV] (IHES Vol. 117, 2013). In particular, under reasonable assumptions on $X$, we…

We prove that the moduli space of stable logarithmic maps with fixed numerical invariants, from logarithmic curves to a fixed projective target logarithmic scheme with fine and saturated logarithmic structure, is a proper algebraic stack.…

In this paper we present an approach to quadratic structures in derived algebraic geometry. We define derived n-shifted quadratic complexes, over derived affine stacks and over general derived stacks, and give several examples of those. We…

We introduce and study module structures on both the dgla of multiplicative vector fields and the graded algebra of functions on Lie groupoids. We show that there is an associated structure of a graded Lie-Rinehart algebra on the vector…

We give a systematic construction of semiorthogonal decompositions of derived categories of coherent sheaves on quasi-smooth derived algebraic stacks over $\mathbb{C}$, where the summands are subcategories defined by weight conditions, and…

In the first part of this paper we construct a model structure for the category of filtered cochain complexes of modules over some commutative ring $R$ and explain how the classical Rees construction relates this to the usual projective…

In this paper, we expand the foundations of derived complex analytic geometry introduced in [DAG-IX] by J. Lurie. We start by studying the analytification functor and its properties. In particular, we prove that for a derived complex scheme…

We prove the representability theorem in derived analytic geometry. The theorem asserts that an analytic moduli functor is a derived analytic stack if and only if it is compatible with Postnikov towers, has a global analytic cotangent…

This is a survey paper on derived symplectic geometry, that will appear as a chapter contribution to the book "New Spaces for Mathematics and Physics", edited by Mathieu Anel and Gabriel Catren. Our goal is to explain how derived stacks can…