29 citations · 65 across the 13 of their papers we have counts for
14 papers
The Hochschild homology of a noncommutative symmetric quotient stack
Rina Anno, Vladimir Baranovsky, Timothy Logvinenko
We prove an orbifold type decomposition theorem for the Hochschild homology of the symmetric powers of a small DG category . In noncommutative geometry, these can be v…
Unbounded twisted complexes
Rina Anno, Timothy Logvinenko
We define unbounded twisted complexes and bicomplexes generalising the notion of a (bounded) twisted complex over a DG category [BK90]. These need to be considered relative to anot…
-structures in monoidal DG categories and strong homotopy unitality
Rina Anno, Sergey Arkhipov, Timothy Logvinenko
We define -structures -- algebras, coalgebras, modules, and comodules -- in an arbitrary monoidal DG category or bicategory by rewriting their definitions in terms of u…
-functors
Rina Anno, Timothy Logvinenko
We propose a new theory of (non-split) P^n-functors. These are F: A -> B for which the adjunction monad RF is a repeated extension of Id_A by powers of an autoequivalence H and thr…
On uniqueness of P-twists
Rina Anno, Timothy Logvinenko
We prove that for any -functor all the convolutions (double cones) of the three-term complex defining its -twis…
Bar category of modules and homotopy adjunction for tensor functors
Rina Anno, Timothy Logvinenko
Given a DG-category A we introduce the bar category of modules Modbar(A). It is a DG-enhancement of the derived category D(A) of A which is isomorphic to the category of DG A-modul…
Exotic t-structures for two-block Springer fibers
Rina Anno, Vinoth Nandakumar
We study the exotic t-structure on the derived category of coherent sheaves on two-block Springer fibre (i.e. for a nilpotent matrix of type (m+n,n) in type A). The exotic t-struct…
Spherical DG-functors
Rina Anno, Timothy Logvinenko
For two DG-categories A and B we define the notion of a spherical Morita quasi-functor A -> B. We construct its associated autoequivalences: the twist T of D(B) and the co-twist F…
Stability conditions for Slodowy slices and real variations of stability
Rina Anno, Roman Bezrukavnikov, Ivan Mirkovic
We provide examples of an explicit submanifold in Bridgeland stabilities space of a local Calabi-Yau, and propose a new variant of definition of stabilities on a triangulated categ…
Orthogonally spherical objects and spherical fibrations
Rina Anno, Timothy Logvinenko
We introduce a relative version of the spherical objects of Seidel and Thomas. Define an object E in the derived category D(Z x X) to be spherical over Z if the corresponding funct…
On adjunctions for Fourier-Mukai transforms
Rina Anno, Timothy Logvinenko
We show that the adjunction counits of a Fourier-Mukai transform from to arise from maps of the kernels of the corresponding Fourier-Mukai transforms. In a ve…
Affine tangles and irreducible exotic sheaves
Rina Anno
We construct a weak representation of the category of framed affine tangles on a disjoint union of triangulated categories . The categories we use are that of co…
Spherical functors
Rina Anno
This paper has been withdrawn and replaced by arXiv:1309.5035. In this paper we describe some examples of so called spherical functors between triangulated categories, which genera…
Multiplicative structure on the Hochschild cohomology of crossed product algebras
Rina Anno
Consider a smooth affine algebraic variety over an algebraically closed field, and let a finite group act on it. We assume that the characteristic of the field is greater t…