We prove an equivalence of two A∞-functors, via Orlov’s Landau–Ginzburg/ Calabi–Yau (LG/CY) correspondence. One is the Polishchuk–Zaslow mirror symmetry functor elliptic curves, and other a localized from Fukaya category T2 to noncommutative matrix factorizations. As corollary, we that LMgrLt realizes homological for any t.

Algebraic topology consists in associating to topological spaces algebraic invariants in order to describe their essential properties. In some (exceptional) cases, it is possible in this way to classify a particular topological space inside a more or less large set of spaces or equivalence classes of spaces, for example up to homotopy equivalence. In the most important cases, a functor is defin...

If Problem 2 is affirmative, then, which functor gives the equivalence ? The following examples suggest that the functor Ψ defined by the fiber product X ×X̄ X + would be a correct one. Examples. (1) ([B-O]): Let X be a smooth quasi-projective variety of dimension 2h−1 which contains a subvarietyM ∼= P with NM/X ∼= O(−1) . One can blow up X along M and blow down the exceptional divisor in anothe...

Building on the fact that descriptive frames are coalgebras for the Vietoris functor on the category of Stone spaces, we introduce and study the concept of a Vietoris bisimulation between two descriptive modal models, together with the associated notion of bisimilarity. We prove that our notion of bisimilarity, which is defined in terms of relation lifting, coincides with Kripke bisimilarity (w...

We decompose the K-theory space of a Waldhausen category in terms of its Dwyer-Kan simplicial localization. This leads to a criterion for functors to induce equivalences of K-theory spectra that generalizes and explains many of the criteria appearing in the literature. We show that under mild hypotheses, a weakly exact functor that induces an equivalence of homotopy categories induces an equiva...

If Problem 2 is affirmative, then, which functor gives the equivalence ? The following examples suggest that the functor Ψ defined by the fiber product X ×X̄ X + would be a correct one. Examples. (1) ([B-O]): Let X be a smooth quasi-projective variety of dimension 2h−1 which contains a subvarietyM ∼= P with NM/X ∼= O(−1) . One can blow up X along M and blow down the exceptional divisor in anothe...

Let R be an Artin algebra and e idempotent of R. Assume that Tor (Re, G) = 0 for any G ∈ Gproj eRe i sufficiently large. Necessary sufficient conditions are given the Schur functor Se to induce a triangle-equivalence ⅅdef(R) ≃ ⅅdef(eRe). Combining this with result Psaroudakis et al. (2014), we provide necessary singular equivalence ⅅsg(R) ⅅsg(eRe) restrict GprojR GprojeRe. Applying these triang...

The classical parabolic induction functor is a fundamental tool on the representation theoretic side of Langlands program. In this article, we study its derived version. It was shown by second author that category smooth G $G$ -representations over k $k$ , p $p$ -adic reductive group and field characteristic equivalent to certain differential graded -algebra H • $H_G^\bullet$ whose zeroth cohom...

We will be concerned here with infinite dimensional representations of a complex semisimple Lie algebra g . In more detail, let Ug be the universal enveloping algebra of g , and let Z(g) be the center of Ug . We consider the category of Ug -modules annihilated by a great enough (unspecified) power of a maximal ideal in Z(g) . It is natural to compare the categories corresponding to two differen...

Preface Motivation Modal logics are usually interpreted through Kripke models, branching logics find their interpretation through models which deal with infinite paths. These seemingly structurally different interpretations can be unified by considering coalgebras which model the underlying worlds suitably; the predicates through which the formulas are represented in their interpretation are mo...