In this paper a method of constructing a semiorthogonal decomposition of the derived category of *G*-equivariant sheaves on a variety *X* is described, provided that the derived category of sheaves on *X *admits a semiorthogonal decomposition, whose components are preserved by the action of the group *G *on *X*. Using this method, semiorthogonal decompositions of equivariant derived categories were obtained for projective bundles and for blow-ups with a smooth center, and also for varieties with a full exceptional collection, preserved by the action of the group. As a main technical instrument, descent theory for derived categories is used.

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Working paper

Here are considered the conditions under which the method of diagrams is liable to include non-classical logics, among which the spatial representation of non-bivalent negation. This will be done with two intended purposes, namely: to review the basic concepts involved in the definition of logical negation; to account for a variety of epistemological obstacles against the introduction of non-classical negations within diagrammatic logic. It will be mainly argued that non-classical logics don't challenge dichotomy as such but merely show that a logical operator may be a negation without operating as a dichotomy.

Added: Nov 4, 2014

Working paper

We analyze whether a depositor’s familiarity with a bank affects depositor behavior during a financial crisis. Familiarity is measured by the presence of regional or local cues in the bank’s name, while depositor behavior is considered in terms of depositor sensitivity to observable bank risk (market discipline exerted by depositors). Using the 2001–2010 bank-level and region-level data for Russia, we show the evidence that depositors use quantity-based discipline on all banks in the sample. The evidence of a price-based discipline mechanism, however, is virtually absent. We find that depositors of familiar banks were less sensitive to bank risk after a financial crisis than depositors at unfamiliar banks. To assure the results are driven by familiarity bias and not implicit support of regional governments to banks with regional cues in their names, we interact the variables with measures of trust in local governments and regional affinity. We find a “flight to familiarity” effect strongly present in regions with strong regional affinity, while the effect is rejected in regions with greater trust in regional and local governments. This suggests that the results are driven by familiarity rather than implicit protection from trusted regional or local governments.

Added: Feb 4, 2017

Working paper

We analyse whether depositor familiarity with a bank affects depositor behaviour during a financial crisis. We measure familiarity by looking for regional or local cues in the bank’s name. We measure depositor behaviour by the their sensitivity to observable bank risk (market discipline). Using 2001–2010 bank-level and region-level data for Russia, we find that depositors of familiar banks become less sensitive to bank risk after a financial crisis relative to depositors of unfamiliar banks. To check that the results are not driven by any implicit support of banks with regional cues in their names by regional governments, but indeed by familiarity bias, we interact the variables of interest with measures of trust in local governments and regional affinity. We find that the flight to familiarity effect is strongly present in regions with strong regional affinity, while the effect is rejected in regions with more trust in regional and local governments. This indicates our results are driven by familiarity and not by any implicit protection from a trusted regional or local government.

Added: Oct 20, 2016

Working paper

In the immediate aftermath of Russia’s 1998 crisis household depositors withdrew money from the insolvent and state-owned Sberbank, despite its unique protection by two explicit government guarantees and its reputation of a repository of trust. This was less the case in well-educated, older, more conservative and remote regions and more so in wealthy, entrepreneurial and central regions, enjoying more media freedom. Survey data confirm that access to free media like NTV turns depositors more vigilant about their banks. Well educated people’s better understanding turns them less likely to run on Sberbank but more likely to run on other banks.

Added: Nov 12, 2013

Working paper

This paper describes a group of derivational verbal suffixes in Abaza, a polysynthetic language belonging to the Northwest Caucasian family. For each suffix I propose a short description of its most remarkable features. In particular, I discuss the polysemy of the refactive and assertive markers and their interaction with the event structure of the verb. Other suffixes such as the putative and inferential markers are interesting due to their peculiar morphological behavior. The diversity of the discussed affixes is tentatively explained by the different pathways of their morphological and semantic development.

Added: Dec 14, 2018

Working paper

Added: Nov 26, 2015

Working paper

We construct a twist-closed enhancement of the derived category of coherent sheaves on a smooth compact complex-analytic manifold by means of DG-category of dbar-superconnections.

Added: Oct 30, 2013

Working paper

Alexeev V.,

arxiv.org. math. Cornell University, 2012
Added: Feb 6, 2013

Working paper

We prove that the derived category D(C) of a generic curve of genus greater than one embeds into the derived category D(M) of the moduli space M of rank two stable bundles on C with fixed determinant of odd degree.

Added: Apr 10, 2017

Working paper

Given a variety Y with a rectangular Lefschetz decomposition of its derived category, we consider a degree n cyclic cover X→Y ramified over a divisor Z⊂Y. We construct semiorthogonal decompositions of D^b(X) and D^b(Z) with distinguished components A_X and A_Z, and prove the equivariant category of A_X (with respect to an action of the n-th roots of unity) admits a semiorthogonal decomposition into n−1 copies of A_Z.

Added: Jan 30, 2015

Working paper

In this paper we study the derived categories of coherent sheaves on Grassmannians Gr(k,n), defined over the ring of integers. We prove that the category D^b(Gr(k,n)) has a semi-orthogonal decomposition, with components being full subcategories of the derived category of representations of GL_k. This in particular implies existence of a full exceptional collection, which is a refinement of Kapranov's collection \cite{Kap}, which was constructed over a field of characteristic zero.
We also describe the right dual semi-orthogonal decomposition which has a similar form, and its components are full subcategories of the derived category of representations of GL_{n−k}. The resulting equivalences between the components of the two decompositions are given by a version of Koszul duality for strict polynomial functors.
We also construct a tilting vector bundle on Gr(k,n). We show that its endomorphism algebra has two natural structures of a split quasi-hereditary algebra over Z, and we identify the objects of D^b(Gr(k,n)), which correspond to the standard and costandard modules in both structures.
All the results automatically extend to the case of arbitrary commutative base ring and the category of perfect complexes on the Grassmannian, by extension of scalars (base change).
Similar results over fields of arbitrary characteristic were obtained independently in \cite{BLVdB}, by different methods.

Added: Feb 2, 2015

Working paper

We study the derived categories of coherent sheaves on Gushel-Mukai varieties. In the derived category of such a variety, we isolate a special semiorthogonal component, which is a K3 or Enriques category according to whether the dimension of the variety is even or odd. We analyze the basic properties of this category using Hochschild homology, Hochschild cohomology, and the Grothendieck group. We study the K3 category of a Gushel-Mukai fourfold in more detail. Namely, we show that this category is equivalent to the derived category of a K3 surface for a certain codimension 1 family of rational fourfolds, and to the K3 category of a birational cubic fourfold for a certain codimension 3 family. The first of these results verifies a special case of a duality conjecture which we formulate. We discuss our results in the context of the rationality problem for Gushel-Mukai varieties, which was one of the main motivations for this work.

Added: May 29, 2016

Working paper

We develop an approach that allows to construct semiorthogonal decompositions of derived categories of surfaces with rational singularities with components equivalent to derived categories of local finite dimensional algebras. First, we discuss how a semiorthogonal decomposition of a resolution of singularities of a surface X may induce a semiorthogonal decomposition of X. In the case when Xhas cyclic quotient singularities, we introduce the condition of adherence for the components of the resolution that allows to identify the components of the induced decomposition with derived categories of explicit local finite dimensional algebras. Further, we present an obstruction in the Brauer group of X to the existence of such semiorthogonal decomposition, and show that in the presence of the obstruction a suitable modification of the adherence condition gives a semiorthogonal decomposition of the twisted derived category of X. We illustrate the theory by exhibiting a semiorthogonal decomposition for the untwisted or twisted derived category of any normal projective toric surface depending on whether its Weil divisor class group is torsion-free or not. Finally, we relate our results to the results of Kawamata based on iterated extensions of reflexive sheaves of rank 1 on X.

Added: Dec 3, 2018

Working paper

We discuss a relation between the structure of derived categories of smooth projective varieties and their birational properties. We suggest a possible definition of a birational invariant, the derived category analogue of the intermediate Jacobian, and discuss its possible applications to the geometry of prime Fano threefolds and cubic fourfolds.

Added: Nov 15, 2015

Working paper

We prove derived equivalence of Calabi–Yau threefolds constructed by Ito–Miura–Okawa– Ueda as an example of non-birational Calabi–Yau varieties whose difference in the Grothendieck ring of varieties is annihilated by the affine line.

Added: Dec 1, 2016

Working paper

In this paper we study derived equivalences for Symplectic reflection algebras. We establish a version of the derived localization theorem between categories of modules over Symplectic reflection algebras and categories of coherent sheaves over quantizations of Q-factorial terminalizations of the symplectic quotient singularities. To do this we construct a Procesi sheaf on the terminalization and show that the quantizations of the terminalization are simple sheaves of algebras. We will also sketch some applications: to the generalized Bernstein inequality and to perversity of wall crossing functors.

Added: Oct 9, 2017

Working paper

Following the approach of Haiden-Katzarkov-Kontsevich arXiv:1409.8611, to any homologically smooth graded gentle algebra A we associate a triple (Σ_A,Λ_A;η_A), where Σ_A is an oriented smooth surface with non-empty boundary, Λ_A is a set of stops on ∂Σ_A and η_A is a line field on Σ_A, such that the derived category of perfect dg-modules of A is equivalent to the partially wrapped Fukaya category of (Σ_A,Λ_A;η_A). Modifying arguments of Johnson and Kawazumi, we classify the orbit decomposition of the action of the (symplectic) mapping class group of Σ_A on the homotopy classes of line fields. As a result we obtain a sufficient criterion for homologically smooth graded gentle algebras to be derived equivalent. Our criterion uses numerical invariants generalizing those given by Avella-Alaminos-Geiss in math/0607348, as well as some other numerical invariants. As an application, we find many new cases when the AAG-invariants determine the derived Morita class. As another application, we establish some derived equivalences between the stacky nodal curves considered in arXiv:1705.06023.

Added: Dec 6, 2018

Working paper

In the world of triangulated categories, categorical resolutions (as defined by Kuznetsov and Luntz) have been useful. One would like to have a similar notion of categorical resolution in homotopical algebra, where one works with categories which are not additive, such as the categories of E_n-algebras. Describing algebraic structures using the approach inspired by Segal, we transfer the question to the setting of homotopical Grothendieck (op)fibrations. We then introduce the notion of derived section of a homotopical Grothendieck (op)fibration, and show that a selected class of functors gives rise to (partial) categorical resolutions for homotopical categories of derived sections.

Added: Dec 23, 2014

Working paper

The aim of this paper is to show how and why the method of radical interpretation, proposed by Donald Davidson, can solve the problems that are formulated in a variety of skeptical scenarios. In particular, the method of radical interpretation deprives Cartesian scenario (both in its traditional and recent versions) all its force and even the status of philosophical problem. Appealing to the difference between intendede and unintended lies one can see how the global skeptical scenario gets solved in both cases. The paper also formulates an argument in favor of expanded version of naturalized epistemology that was offered by W. V. O. Quine - first of all, due to the introduction of social factors. In particualr, there are always at least two necessary limitations imposed by the communication on our hypothesis about knowledge and delusion. In addition, the paper explains the need for a moderate externalism (both perceptual and social) to the variants of Descartes and Hume's skeptical scenario.

Added: Apr 26, 2014

Working paper

Proposed study aims to clarify the nature of the rationality crisis in the European culture of Modernity. This crisis manifested itself in many ways already in the 17th-19th centuries, i.e. at the peak of rationalism. The study considers certain aspects of Cartesianism, which prevented it from dissolving entirely in the epistemology and methodology of Modernity and which, moreover, presuppose certain steps to be taken toward reconsidering the new European rationalism within the framework of overlapping philosophical ideas and literary images. The study focuses on three subjects implied by ‘cogito’: self-consciousness, will, and law.

Added: Apr 6, 2015

Working paper

Added: Sep 10, 2012