ar X iv : m at h / 01 03 07 5 v 1 [ m at h . R A ] 1 3 M ar 2 00 1 RESIDUE COMPLEXES OVER NONCOMMUTATIVE RINGS

ar X iv : m at h / 01 03 07 5 v 3 [ m at h . R A ] 3 J un 2 00 2 RESIDUE COMPLEXES OVER NONCOMMUTATIVE RINGS

Residue complexes were introduced by Grothendieck in algebraic geometry. These are canonical complexes of injective modules that enjoy remarkable functorial properties (traces). In this paper we study residue complexes over noncommutative rings. These objects have a more intricate structure than in the commutative case, since they are complexes of bimodules. We develop methods to prove uniquene...

ar X iv : m at h / 01 03 07 5 v 2 [ m at h . R A ] 1 8 Ju n 20 01 RESIDUE COMPLEXES OVER NONCOMMUTATIVE RINGS

Residue complexes were introduced by Grothendieck in algebraic geometry. These are canonical complexes of injective modules that enjoy remarkable functorial properties (traces). In this paper we study residue complexes over noncommutative rings. These objects have a more intricate structure than in the commutative case, since they are complexes of bimodules. We develop methods to prove uniquene...

ar X iv : m at h / 03 12 22 1 v 1 [ m at h . R A ] 1 1 D ec 2 00 3 three talks on noncommutative geometry

ar X iv : m at h / 06 03 73 3 v 1 [ m at h . A C ] 3 1 M ar 2 00 6 RIGID COMPLEXES VIA DG ALGEBRAS

Let A be a commutative ring, B a commutative A-algebra and M a complex of B-modules. We begin by constructing the square SqB/A M , which is also a complex of B-modules. The squaring operation is a quadratic functor, and its construction requires differential graded (DG) algebras. If there exists an isomorphism ρ : M ≃ −→ SqB/A M then the pair (M,ρ) is called a rigid complex over B relative to A...

ar X iv : m at h - ph / 0 10 30 34 v 1 2 5 M ar 2 00 1 MZ - TH 01 - 09 LPT - ORSAY 01 - 28 MULTIPLE NONCOMMUTATIVE TORI

We derive the Kac-Paljutkin finite-dimensional Hopf algebras as finite fibrations of the quantum double torus and generalize the construction for quantum multiple tori.