Related papers: Riemann-Hilbert correspondence for mixed twistor D…

When formulated in twistor space, the D-instanton corrected hypermultiplet moduli space in N=2 string vacua and the Coulomb branch of rigid N=2 gauge theories on $R^3 \times S^1$ are strikingly similar and, to a large extent, dictated by…

We determine the regular irreducible components of the variety mod(A,d), where A=kQ/I is a string algebra and I is generated by a set of paths of length two. Our case is among the first examples of descriptions of irreducible components,…

We extend the relation between quasi-modular forms and modular forms to a wider class of functions. We then relate both forms to vector-valued modular forms with symmetric power representations, and prove a general structure theorem for…

Given a Hopf algebra H, we study modules and bimodules over an algebra A that carry an H-action, as well as their morphisms and connections. Bimodules naturally arise when considering noncommutative analogues of tensor bundles. For…

The paper is devoted to study some of the questions arises naturally in connection to the notion of relative derived categories. In particular, we study invariants of recollements involving relative derived categories, generalise two…

Let R be a regular ring essentially of finite type over a perfect field k. An R-module M is called a unit R[F]-module if it comes equipped with an isomorphism F*M-->M where F denotes the Frobenius map on Spec R, and F* is the associated…

Let W be a smooth complex quasiprojective variety with the action of a connected reductive group G. Adapting the stratification approach of Teleman to a microlocal context, we prove a vanishing theorem for the functor of G-invariant…

The dihedral homology functor $HD:A_\infty^{{\rm inv}}(K)\to GrM(K)$ from the category $A_\infty^{{\rm inv}}(K)$ of involutive $A_\infty$-algebras over any commutative unital ring $K$ to the category $GrM(K)$ of graded $K$-modules is…

We develop the $L$-functions ratios conjecture with one shift in the numerator and denominator in certain ranges for the family of quadratic twist of modular $L$-functions using multiple Dirichlet series under the generalized Riemann…

We present a definition of a (super)-modular functor which includes certain interesting cases that previous definitions do not allow. We also introduce a notion of topological twisting of a modular functor, and construct formally a…

Let E be a (right) Hilbert C*-module over a C*-algebra A. If E is equipped with a left action of a second C*-algebra B, then tensor product with E gives rise to a functor from the category of Hilbert B-modules to the category of Hilbert…

We compare and contrast various relative cohomology theories that arise from resolutions involving semidualizing modules. We prove a general balance result for relative cohomology over a Cohen-Macaulay ring with a dualizing module, and we…

We introduce the notion of noncompact (partial) silting and (partial) tilting sets and objects in any triangulated category D with arbitrary (set-indexed) coproducts. We show that equivalence classes of partial silting sets are in bijection…

We review the theory of quaternionic Kahler and hyperkahler structures. Then we consider the tangent bundle of a Riemannian manifold M with a metric connection D (with torsion) and with its well estabilished canonical complex structure.…

We show that the Fourier-Laplace transform of an irreducible regular differential system on the Riemann sphere underlies, when one only considers the part at finite distance, a polarizable regular twistor $\mathcal{D}$-module. The…

Holm (H. Holm, Modules with cosupport and injective functors, Algebr. Represent. Theor., 13 (2010), 543-560) considers categories of right modules dual to those with support in a set of finitely presented modules. We extend some of his…

We develop a theory of tdos and twisted $\mathcal D$-modules over general base schemes with a focus on functorial aspects. In particular, we introduce a flat base change functor and establish its compatibility with globalization and direct…

Higher homological algebra, basically done in the framework of an $n$-cluster tilting subcategory $\mathcal{M}$ of an abelian category $\mathcal{A}$, has been the topic of several recent researches. In this paper, we study a relative…

Motivated by an equivalence of categories established by Kapranov and Schechtman, we introduce, for each non-negative integer d, the category of connected bialgebras modulo d+1. We show that these categories fit into an inverse system of…

Let $\mathcal{V}$ be a mixed characteristic complete discrete valuation ring, $\mathcal{P}$ a separated smooth formal scheme over $\mathcal{V}$, $P$ its special fiber, $X$ a smooth closed subscheme of $P$, $T$ a divisor in $P$ such that…