We strengthen a result of Hanke-Schick about the strong Novikov conjecture for low degree cohomology by showing that their non-vanishing maximal group C*-algebra holds many other exotic C*-algebras, in particular one associated to smallest strongly Morita compatible and exact crossed product functor used new version Baum-Connes conjecture. To achieve this we provide Fell absorption principle ce...

We introduce several classes of localizations (idempotent monads) on the category groups and study their properties relations. The most interesting class for us is which coincide with zero derived functors. call them right exact (in sense Keune). prove that a localization L preserves nilpotent finite p-group G map → LG an epimorphism. also some examples (Baumslag’s P-localization respect to set...

We exhibit examples of triangulated categories which are neither the stable category of a Frobenius category nor a full triangulated subcategory of the homotopy category of a stable model category. Even more drastically, our examples do not admit any non-trivial exact functors to or from these algebraic respectively topological triangulated categories. Introduction. Triangulated categories are ...

This paper is devoted to deformation theory of "anabelian" representations of the absolute Galois group landing in outer automorphism group of the algebraic fundamental group of a hyperbolic smooth curve defined over a number-field. In the first part of this paper, we obtained several universal deformations for Lie-algebra versions of the above representation using the Schlessinger criteria for...

Abstract We prove a product formula for the determinant of cohomology an étale sheaf with $\ell $ -adic coefficients over arbitrary proper scheme perfect field positive characteristic p distinct from . The local contributions are constructed by iterating vanishing cycle functors as well certain exact additive that can be considered linearised versions Artin conductors and $\varepsilon -factors....

Exact squares in Cat are not necessarily absolute (i.e. preserved by any 2-functor Cat→ Cat), or even preserved by any 2-functor given by exponentiation (−)I : Cat → Cat: if a square is preserved by exponentiation it will be called a contractible exact square. We will characterize diagrammatically these contractible squares, and among them the contractible categories, and the so called fibering...

1.1. Definition. Let C be an abelian category. The derivative D(C) of C is defined as follows: The objects are exact sequences 0 −→ X0 iX −−→ X1 πX −−→ X0 −→ 0 of C, and the morphisms from such an object are morphisms of exact sequences whose two X parts coincide. The category D(C) is again abelian. An exact functor F : C1 −→ C2 gives rise to an induced (exact) functor D(F ) : D(C1) −→ D(C2). W...

We use Grayson’s binary multicomplex presentation of algebraic K-theory to give a new construction of exterior power operations on the higher K-groups of a (quasi-compact) scheme. We show that these operations satisfy the axioms of a λ-ring, including the product and composition laws. To prove the composition law we show that the Grothendieck group of the exact category of integral polynomial f...

The aim of these Notes is to introduce the reader to the language of categories with emphazis on homological algebra. We treat with some details basic homological algebra, that is, categories of complexes in additive and abelian categories and construct with some care the derived functors. We also introduce the reader to the more sophisticated concepts of triangulated and derived categories. Ou...

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...