Related papers: C-Constructible Enhanced Ind-Sheaves

In this paper, we prove that any perfect complex of $D^{\infty}$-modules may be reconstructed from its holomorphic solution complex provided that we keep track of the natural topology of this last complex. This is to be compared with the…

We introduce and study the category of twisted modules over a triangular differential graded bocs. We show that in this category idempotents split, that it admits a natural structure of a Frobenius category, that a twisted module is…

We introduce the notion of a holonomic D-module on a smooth (idealized) logarithmic scheme and show that Verdier duality can be extended to this context. In contrast to the classical case, the pushforward of a holonomic module along an open…

A morphism of the moduli functor of admissible semistable pairs to the Gieseker -- Maruyama moduli functor (of semistable coherent torsion-free sheaves) with the same Hilbert polynomial on the surface, is constructed. It is shown that these…

The category of character D-modules is realized as Drinfeld center of the abelian monoidal category of Harish-Chandra bimodules. Tensor product of Harish-Chandra bimodules is related to convolution of D-modules via the long intertwining…

This paper proves that the functor $C(*)$ that sends pointed, simply-connected CW-complexes to their chain-complexes equipped with diagonals and iterated higher diagonals, determines their integral homotopy type --- even inducing an…

We associate a t-structure to a family of objects in D(A), the derived category of a Grothendieck category A. Using general results on t-structures, we give a new proof of Rickard's theorem on equivalence of bounded derived categories of…

The derived category $D[C,V]$ of the Grothendieck category of enriched functors $[C,V]$, where $V$ is a closed symmetric monoidal Grothendieck category and $C$ is a small $V$-category, is studied. We prove that if the derived category…

Let $X$ be a real analytic manifold, and let $T^*X$ be its cotangent bundle. In a recent paper with E. Zaslow \cite{NZ}, we showed that the dg category $Sh_c(X)$ of constructible sheaves on $X$ quasi-embeds into the triangulated envelope…

Let $R$ be a polynomial ring over a field $K$ of arbitrary characteristic and $D$ be the ring of differential operators over $R$. Inspired by Euler formula for homogeneous polynomials, we introduce a class of graded $D$-modules, called…

In this paper, we prove that given a differential graded category C and B a full differential graded subcategory closed under coproducts, there is a canonical recollement of differential graded categories, for which we use enriched…

We introduce the notion of regularity for a relative holonomic $\mathcal D$-module in the sense of arXiv:1204.1331. We prove that the solution functor from the bounded derived category of regular relative holonomic modules to that of…

We show that if $\alpha$ is a regular cardinal, $\mathcal{D}$ is an $\alpha$-compactly generated triangulated category, in the sense of Neeman \cite{N}, and $\tau$ is a t-structure in $\mathcal{D}$ generated by a set of $\alpha$-compact…

We construct an "almost involution" assigning a new DG-category to a given one, and use this construction to recover, say, the abelian category of graded modules over the graded ring $R^*$ from the DG-category of DG-modules over a DG-ring…

In arXiv:1001.2562 a certain non-commutative algebra $A$ was defined starting from a semi-simple algebraic group, so that the derived category of $A$-modules is equivalent to the derived category of coherent sheaves on the Springer (or…

In a compactly generated triangulated category, we introduce a class of tilting objects satisfying certain purity condition. We call these the decent tilting objects and show that the tilting heart induced by any such object is equivalent…

Graded Hecke algebras can be constructed in terms of equivariant cohomology and constructible sheaves on nilpotent cones. In earlier work, their standard modules and their irreducible modules where realized with such geometric methods. We…

We define the Chow $t$-structure on the $\infty$-category of motivic spectra $SH(k)$ over an arbitrary base field $k$. We identify the heart of this $t$-structure $SH(k)^{c\heartsuit}$ when the exponential characteristic of $k$ is inverted.…

We present a uniform theory of constructible sheaves on arbitrary schemes with coefficients in topological or even condensed rings. This is accomplished by defining lisse sheaves to be the dualizable objects in the derived infinity-category…

We present a detailed introduction of the theory of constructible sheaf complexes in the complex algebraic and analytic setting. All concepts are illustrated by many interesting examples and relevant applications, while some important…