Related papers: Tannaka duality revisited
Applying a general categorical construction for the extension of dualities, we present a new proof of the Fedorchuk duality between the category of compact Hausdorff spaces with their quasi-open mappings and the category of complete normal…
We exploit singular equivalences between artin algebras, that are induced from certain functors between the stable module categories. Such functors are called pre-triangle equivalences. We construct two pre-triangle equivalences connecting…
We show that every complete intersection of Laurent polynomials in an algebraic torus is isomorphic to a complete intersection of master functions in the complement of a hyperplane arrangement, and vice versa. We call this association Gale…
Plonka sums consist of an algebraic construction similar, in some sense to direct limits, which allows to represent classes of algebras defined by means of regular identities (namely those equations where the same set of variables appears…
The notion of a duality between two derived functors as well as an extension theorem for derived functors to larger categories in which they need not be defined is introduced. These ideas are then applied to extend and study the coext…
Associated to any closed quantum subgroup $G\subset U_N^+$ and any index set $I\subset\{1,\ldots,N\}$ is a certain homogeneous space $X_{G,I}\subset S^{N-1}_{\mathbb C,+}$, called affine homogeneous space. We discuss here the abstract…
We define a differential Tannakian category and show that under a natural assumption it has a fibre functor. If in addition this category is neutral, that is, the target category for the fibre functor are finite dimensional vector spaces…
This paper is a complement to the paper "On $p$-adic differential equations on semistable varieties" written by V. Di Proietto. Given an open variety over a DVR with semistable reduction, the author constructed in that paper a fully…
We prove a comparison result between two duality statements - Takai duality, which is implemented by the crossed product functor $- \rtimes G: KK^{G} \to KK^{\hat G}$ on equivariant Kasparov categories; and Treumann duality, which asserts…
Consider the wrapped Fukaya category W of a collection of exact Lagrangians in a Liouville manifold. Under a non-degeneracy condition implying the existence of enough Lagrangians, we show that natural geometric maps from the Hochschild…
We use Tannakian methods to show that patching for coherent sheaves implies patching for objects in any Noetherian algebraic stack with affine stabilizers. Among other things, this gives a straightforward way to prove patching for torsors…
In this paper we will describe an approach to mirror symmetry for appropriate 1-dimensional DM stacks of arithmetic genus $g \leq 1$, called tcnc curves, which was developed by the author with Treumann and Zaslow in arXiv:1103.2462 . This…
Twinlike defects refer to topological defect solutions of some apparently different field models that share the same defect configuration and the same energy density. Usually, one can distinguish twinlike defects in terms of their linear…
In this paper, we prove the integrality conjecture for quotient stacks arising from weakly symmetric representations of reductive groups. Our main result is a decomposition of the cohomology of the stack into finite-dimensional components…
This paper surveys some recent results about Fourier--Mukai functors. In particular, given an exact functor between the bounded derived categories of coherent sheaves on two smooth projective varieties, we deal with the question whether…
Classical invariants for representations of one Lie group can often be related to invariants of some other Lie group. Physics suggests that the right objects to consider for these questions are certain refinements of classical invariants…
We develop a semistability algorithm for vector bundles which are given as a kernel of a surjective morphism between splitting bundles on the projective space over an algebraically closed field K. This class of bundles is a generalization…
In this short work we give a very short and elementary proof of the injectivity lemma, which plays an important role in the Tannakian duality for Hopf algebras over a field. Based on this we provide some generalizations of this fact to the…
The main result of this paper is that, off of a `fundamental class' in degree 1, the linearized Legendrian contact homology obeys a version of Poincare duality between homology groups in degrees k and -k. Not only does the result itself…
We prove that every commutative differential graded algebra whose cohomology is a simply-connected Poincare duality algebra is quasi-isomorphic to one whose underlying algebra is simply-connected and satisfies Poincare duality in the same…