Related papers: Reciprocity sheaves, II
We revisit sheaves on locales by placing them in the context of the theory of quantale modules. The local homeomorphisms $p:X\to B$ are identified with the Hilbert $B$-modules that are equipped with a natural notion of basis. The…
We associate a two-sided cell to any (parabolic) character sheaf. We study the interaction of the duality operator for character sheaves and the operation of "twisted induction".
We survey recent advances in the theory of moduli spaces of stable sheaves on hyperk\"ahler manifolds of dimension greater than $2$. We start by recalling the well-known theory in dimension $2$, i.e.~for $K3$ surfaces, emphasizing the…
We study rank-two reflexive sheaves on $\mathbb{P}^3$ with $c_2 =4$, expanding on previous results for $c_2\le3$. We show that every spectrum not previously ruled out is realized. Moreover, moduli spaces are studied and described in detail…
Reciprocity is a second-order correlation that has been recently detected in all real directed networks and shown to have a crucial effect on the dynamical processes taking place on them. However, no current theoretical model generates…
In [arXiv:2109.13991], the author explained a relation between enhanced ind-sheaves and enhanced subanalytic sheaves. In this paper, we shall define C-constructability for enhanced subanalytic sheaves which was announced in…
We give a sharp construction for twins in arbelos, based on polar reciprocity. In the process, new circles displaying arquimedean afinities came into scene.
We relate R-equivalence on tori with Voevodsky's theory of homotopy invariant Nisnevich sheaves with transfers and effective motivic complexes.
Moduli spaces of stable sheaves on smooth projective surfaces are in general singular. Nonetheless, they carry a virtual class, which -- in analogy with the classical case of Hilbert schemes of points -- can be used to define intersection…
We study stacks of slope-semistable twisted sheaves on orbisurfaces with projective coarse spaces and prove that in certain cases they have many of the asymptotic properties enjoyed by the moduli of slope-semistable sheaves on smooth…
It is well known that numerical quantities arising from the theory of D-modules are related to invariants of singularities in birational geometry. This paper surveys a deeper relationship between the two areas, where the numerical…
In this paper we develop the theory of perverse sheaves on Artin stacks continuing the study in "The six operations for sheaves on Artin stacks I: Finite Coefficients" and "The six operations for sheaves on Artin stacks II: Adic…
All types of networks arise as intricate combinations of dyadic building blocks formed by pairs of vertices. In directed networks, the dyadic patterns are entirely determined by reciprocity, i.e. the tendency to form, or to avoid, mutual…
We study non-commutative projective lines over not necessarily algebraic bimodules. In particular, we give a complete description of their categories of coherent sheaves and show they are derived equivalent to certain bimodule species. This…
We relate the category of sheaves on alcoves that was constructed in "Sheaves on the alcoves and modular representations I" to the representation theory of reductive algebraic groups. In particular, we show that its indecomposable…
We introduce a notion of stability for sheaves with respect to several polarisations that generalises the usual notion of Gieseker-stability. We prove, under a boundedness assumption, which we show to hold on threefolds or for rank two…
We give a formalism of mixed sheaves on varieties over a subfield of the complex number field.
This is the first of two papers studying moduli spaces of a certain class of coherent sheaves, which we call {\it stable perverse coherent sheaves}, on the blowup of a projective surface. They are used to relate usual moduli spaces of…
Associated varieties of vertex algebras are analogue of the associated varieties of primitive ideals of the universal enveloping algebras of semisimple Lie algebras. They not only capture some of the important properties of vertex algebras…
We introduce a new method for ``twisting'' relative equivalences of derived categories of sheaves on two spaces over the same base. The first aspect of this is that the derived categories of sheaves on the spaces are twisted. They become…