Equivariant KK-theory and the Novikov conjecture.
Let be a ring. In two previous articles [12, 14] we studied the homotopy category of projective -modules. We produced a set of generators for this category, proved that the category is -compactly generated for any ring , and showed that it need not always be compactly generated, but is for sufficiently nice . We furthermore analyzed the inclusion and the orthogonal subcategory . And we even showed that the inclusion has a right adjoint; this forces some natural map to be an equivalence...
Soient un anneau commutatif et une -algèbre associative quelconque. Nous calculons le groupe d’homologie de la -algèbre de Lie des matrices de “trace nulle” sur . Le groupe ainsi déterminé est un groupe d’homologie d’un complexe inspiré d’A. Connes; il est isomorphe à lorsque est commutative. Nous obtenons également des résultats pour un groupe d’homologie relative associé à une surjection de -algèbres. Les démonstrations utilisent la classification des extensions centrales et des...
A subsheaf of the sheaf of germs functions over an open subset of is called a sheaf of sub function. Comparing with the investigations of sheaves of ideals of , we study the finite presentability of certain sheaves of sub -rings. Especially we treat the sheaf defined by the distribution of Mather’s -classes of a mapping.