Related papers: A Mapping Theorem for Derived Foliations

We construct $S$-linear semiorthogonal decompositions of derived categories of smooth Fano threefold fibrations $X/S$ with relative Picard rank $1$ and rational geometric fibers and discuss how the structure of components of these…

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 provide a semiorthogonal decomposition for the derived category of fibrations of quintic del Pezzo surfaces with rational Gorenstein singularities. There are three components, two of which are equivalent to the derived categories of the…

Multiparameter persistent homology has emerged as a powerful generalization of topological data analysis, capable of encoding multivariate filtrations. However, the algebraic complexity of multiparameter persistence modules, marked by wild…

We construct a family of oriented extended topological field theories using the AKSZ construction in derived algebraic geometry, which can be viewed as an algebraic and topological version of the classical AKSZ field theories that occur in…

We show that if a smooth multiplicative subbundle $S\subseteq TG$ on a groupoid $G\rr P$ is involutive and satisfies completeness conditions, then its leaf space $G/S$ inherits a groupoid structure over the space of leaves of $TP\cap S$ in…

This paper presents a survey on formal moduli problems. It starts with an introduction to pointed formal moduli problems and a sketch of proof of a Theorem (independently proven by Lurie and Pridham) which gives a precise mathematical…

In arXiv:2011.08830 we established a series of correspondences relating five enumerative theories of log Calabi-Yau surfaces, i.e. pairs $(Y,D)$ with $Y$ a smooth projective complex surface and $D=D_1+\dots +D_l$ an anticanonical divisor on…

Let $X$, $Y$ be smooth projective varieties over $\mathbf{C}$. Let $K$ be a bounded complex of coherent sheaves on $X\times Y$ and let $\Phi_K \colon \mathsf{D}^b_{\mathsf{Coh}}(X) \to \mathsf{D}^b_{\mathsf{Coh}}(Y)$ be the resulting…

We study a notion of derived foliations on schemes and derived schemes of arbitrary characteristics. We introduce the Hodge filtration associated to a derived foliation, which functorialy filters derived de Rham cohomology. We use this…

We construct a proper moduli space which is a Deligne-Mumford stack parametrising quasimaps relative to a simple normal crossings divisor in any genus using logarithmic geometry. We show this moduli space admits a virtual fundamental class…

In this note we present a work in progress whose main purpose is to establish a categorified version of sheaf theory. We present a notion of derived categorical sheaves, which is a categorified version of the notion of complexes of sheaves…

This paper investigates the derived and spectral analogs of logarithmic geometry. We develop the deformation theory for animated log rings and $\mathbb{E}_\infty$-log rings and examine the corresponding theories of derived and spectral log…

Huybrechts and Thomas recently constructed relative obstruction theory of objects of the derived category of coherent sheaves over smooth projective family. In this paper, we use this construction to obtain the absolute…

Given a smooth variety $X$ with an action of a finite group $G$, and a semiorthogonal decomposition of the derived category, $\mathcal{D}([X/G])$, of $G$-equivariant coherent sheaves on $X$ into subcategories equivalent to derived…

For conformal geometries of Riemannian signature, we provide a comprehensive and explicit treatment of the core local theory for embedded submanifolds of arbitrary dimension. This is based in the conformal tractor calculus and includes a…

We prove the existence of the dualizing functor for a separated morphism of algebraic stacks with affine diagonal; then we explicitly develop duality for compact Deligne-Mumford stacks focusing in particular on the morphism from a stack to…

The goal of this paper is to show that Stokes data coming from flat bundles form a locally geometric derived stack locally of finite presentation. This generalizes existing geometricity results on Stokes data in four different directions:…

We propose a geometric and categorical approach to the Hodge Conjecture for all smooth projective complex varieties. By embedding any such variety into a flat family with general fibers smooth complete intersections, we prove the conjecture…

Several possible presentations for the homotopy theory of (non-hypercomplete) $\infty$-stacks on a classical site S are discussed. In particular, it is shown that an elegant combinatorial description in terms of diagrams in S exists,…