79 citations · 302 across the 13 of their papers we have counts for
19 papers
Lagrangian Floer theory for trivalent graphs and homological mirror symmetry for curves
Denis Auroux, Alexander I. Efimov, Ludmil Katzarkov
Mirror symmetry for higher genus curves is usually formulated and studied in terms of Landau-Ginzburg models; however the critical locus of the superpotential is arguably of greate…
Categorical smooth compactifications and generalized Hodge-to-de Rham degeneration
Alexander I. Efimov
We disprove two (unpublished) conjectures of Kontsevich which state generalized versions of categorical Hodge-to-de Rham degeneration for smooth and for proper DG categories (but n…
Categorical formal punctured neighborhood of infinity, I
Alexander I. Efimov
In this paper we introduce and study the formal punctured neighborhood of infinity, both in the algebro-geometric and in the DG categorical frameworks. For a smooth algebraic varie…
Some remarks on L-equivalence of algebraic varieties
Alexander I. Efimov
In this short note we study the questions of (non-)L-equivalence of algebraic varieties, in particular, for abelian varieties and K3 surfaces. We disprove the original version of a…
Generalized non-commutative degeneration conjecture
Alexander I. Efimov
In this paper we propose a generalization of the Kontsevich--Soibelman conjecture on the degeneration of Hochschild-to-cyclic spectral sequence for smooth and compact DG category.…
Mac Lane (co)homology of the second kind and Wieferich primes
Alexander I. Efimov
In this paper we investigate the connection between the Mac Lane (co)homology and Wieferich primes in finite localizations of global number rings. Following the ideas of Polishchuk…
Derived categories of Grassmannians over integers and modular representation theory
Alexander I. Efimov
In this paper we study the derived categories of coherent sheaves on Grassmannians defined over the ring of integers. We prove that the category $D^b(\ope…
Homotopy finiteness of some DG categories from algebraic geometry
Alexander I. Efimov
In this paper, we prove that the bounded derived category of coherent sheaves on a separated scheme of finite type over a field of characteristic ze…
Quantum cluster variables via vanishing cycles
Alexander I. Efimov
In this paper, we provide a Hodge-theoretic interpretation of Laurent phenomenon for general skew-symmetric quantum cluster algebras, using Donaldson-Thomas theory for a quiver wit…
Cohomological Hall algebra of a symmetric quiver
Alexander I. Efimov
In the paper \cite{KS}, Kontsevich and Soibelman in particular associate to each finite quiver with a set of vertices the so-called Cohomological Hall algebra $\cH,$ which…
Homological mirror symmetry for punctured spheres
Mohammed Abouzaid, Denis Auroux, Alexander I. Efimov +2
We prove that the wrapped Fukaya category of a punctured sphere ( with an arbitrary number of points removed) is equivalent to the triangulated category of singularities of a…
Coherent analogues of matrix factorizations and relative singularity categories
Alexander I. Efimov, Leonid Positselski
We define the triangulated category of relative singularities of a closed subscheme in a scheme. When the closed subscheme is a Cartier divisor, we consider matrix factorizations o…
Maximal lengths of exceptional collections of line bundles
Alexander I. Efimov
In this paper we construct infinitely many examples of toric Fano varieties with Picard number three, which do not admit full exceptional collections of line bundles. In particular…
Formal completion of a category along a subcategory
Alexander I. Efimov
Following an idea of Kontsevich, we introduce and study the notion of formal completion of a compactly generated (by a set of objects) enhanced triangulated category along a full t…
A proof of Kontsevich-Soibelman conjecture
Alexander I. Efimov
It is well known that "Fukaya category" is in fact an -pre-category in sense of Kontsevich and Soibelman \cite{KS}. The reason is that in general the morphism spaces ar…
Homological mirror symmetry for curves of higher genus
Alexander I. Efimov
Katzarkov has proposed a generalization of Kontsevich's mirror symmetry conjecture, covering some varieties of general type. Seidel \cite{Se} has proved a version of this conjectur…
Deformation theory of objects in homotopy and derived categories III: abelian categories
Alexander I. Efimov, Valery A. Lunts, Dmitri O. Orlov
This is the third paper in a series. In part I we developed a deformation theory of objects in homotopy and derived categories of DG categories. Here we show how this theory can be…
Deformation theory of objects in homotopy and derived categories II: pro-representability of the deformation functor
Alexander I. Efimov, Valery A. Lunts, Dmitri O. Orlov
This is the second paper in a series. In part I we developed deformation theory of objects in homotopy and derived categories of DG categories. Here we extend these (derived) defor…
Deformation theory of objects in homotopy and derived categories I: general theory
Alexander I. Efimov, Valery A. Lunts, Dmitri O. Orlov
This is the first paper in a series. We develop a general deformation theory of objects in homotopy and derived categories of DG categories. Namely, for a DG module over a DG c…