In this paper, we give a proof of homological mirror symmetry for two variable invertible polynomials, where the group on $B$-side is taken to be maximal. The involves an explicit gluing construction Milnor fibres, and as application, prove derived equivalences between certain nodal stacky curves, some whose irreducible components have non-trivial generic stabiliser.

We investigate the Galois coverings of piecewise algebras and more particularly their behaviour under derived equivalences. Under a technical assumption which is satisfied if the algebra is derived equivalent to a hereditary algebra, we prove that there exists a universal Galois covering whose group of automorphisms is free and depends only on the derived category of the algebra. As a corollary...

We give a complete derived equivalence classification of all symmetric algebras of domestic representation type over an algebraically closed field. This completes previous work by R. Bocian and the authors, where in this paper we solve the crucial problem of distinguishing standard and nonstandard algebras up to derived equivalence. Our main tool are generalized Reynolds ideals, introduced by B...

"Starting with group graded Morita equivalences, we obtain equivalences for tensor products and wreath products."

We give the first examples of derived equivalences between varieties defined over non-closed fields where one has a rational point and other does not. begin with torsors Jacobians curves Q F_q(t), conclude pair hyperkaehler 4-folds Q. The latter is independently interesting as new example transcendental Brauer-Manin obstruction to Hasse principle.

We show that K1(E) of an exact category E agrees with K1(DE) of the associated triangulated derivator DE. More generally we show that K1(W) of a Waldhausen category W with cylinders and a saturated class of weak equivalences agrees with K1(DW) of the associated right pointed derivator DW. Introduction For a long time there was an interest in defining a nice K-theory for triangulated categories ...

Weak equivalences are important behavioral equivalences in the course of specifying and analyzing the reactive systems using process algebraic languages. In this paper, we propose a series of weak equivalences named weak parametric failure equivalences, which take two previously-known behavioral equivalences, i.e., the weak failure equivalence and the weak impossible future equivalence, as thei...

Abstract We study the equivariant category associated to a finite group action on derived of coherent sheaves smooth projective variety. In particular, we discuss decompositions category, prove existence Serre functor, and give criterion for be Calabi–Yau. describe an obstruction subgroup auto-equivalences act category. As application show that any Calabi–Yau elliptic curve is equivalent curve.

We give a complete description of the Morita equivalence classes of blocks with elementary abelian defect groups of order 8 and of the derived equivalences between them. A consequence is the verification of Broué’s abelian defect group conjecture for these blocks. It also completes the classification of Morita and derived equivalence classes of 2-blocks of defect at most three defined over a su...