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Local cohomology and support for triangulated categories

Dave Benson, Srikanth B. Iyengar, Henning Krause (2008)

Annales scientifiques de l'École Normale Supérieure

We propose a new method for defining a notion of support for objects in any compactly generated triangulated category admitting small coproducts. This approach is based on a construction of local cohomology functors on triangulated categories, with respect to a central ring of operators. Special cases are, for example, the theory for commutative noetherian rings due to Foxby and Neeman, the theory of Avramov and Buchweitz for complete intersection local rings, and varieties for representations of...

Localizing groups with action.

Georg Peschke (1989)

Publicacions Matemàtiques

When localizing the semidirect product of two groups, the effect on the factors is made explicit. As an application in Topology, we show that the loop space of a based connected CW-complex is a P-local group, up to homotopy, if and only if π1X and the free homotopy groups [Sk-1, ΩX], k ≥ 2, are P-local.

Loop spaces and homotopy operations

David Blanc (1997)

Fundamenta Mathematicae

We describe an obstruction theory for an H-space X to be a loop space, in terms of higher homotopy operations taking values in π * X . These depend on first algebraically “delooping” the Π-algebras π * X , using the H-space structure on X, and then trying to realize the delooped Π-algebra.

LS-catégorie de CW-complexes à 3 cellules en théorie homototique R-locale.

Hans Scheerer, Daniel Tanré (1997)

Publicacions Matemàtiques

We study the Lusternik-Schnirelmann category of some CW-complexes with 3 cells, built on Y = S2n Uk[i2n,i2n] e4n. In particular, we prove that an R-local space, in the sense of D. Anick, of LS-category 3 and of the homotopy type of a CW-complex with 3 R-cells, has a cup-product of length 3 in its algebra of cohomology. This result is no longer true in the framework of mild spaces.

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