Local cohomology,cofiniteness and homological functors of modules

Czechoslovak Mathematical Journal - Let I be an ideal of a commutative Noetherian ring R. It is shown that the R-modules H (M) are I-cofinite for all finitely generated R-modules M and all j...     

A generalization of certain homological functors

Summary By a natural process of relativization groups Extⁿ(A, φ), π_n(A, φ) are defined in any abelian category with sufficient injectives and projectives. Functoriality in φ i spro. ved and excision properties are established; and the groups are shown to behave well under suspension. The technique involves an interplay of different mapping-cone constructions In memory of Guido Castelnuovo, on the occasion of the first centenary of his birth.     

Strict polynomial functors and coherent functors

We build an explicit link between coherent functors in the sense of Auslander [Coherent functors. Proc. Conf. Categorical Algebra (La Jolla, Calif., 1965). Springer, Berlin, pp. 189–231, 1966] and strict polynomial functors in the sense of Friedlander and Suslin (Invent. Math. 127(2), 209–270, 1997). Applications to functor cohomology are discussed. V. Franjou is partially supported by the LMJL—Laboratoire de Mathématiques Jean Leray, CNRS: Université de Nantes, école Centrale de Nantes, and acknowledges the hospitality and support of CRM Barcelona where the final corrections on this paper were implemented.     

Rhetorical biset functors,rational p-biset functors and their semisimplicity in characteristic zero

Rhetorical biset functors can be defined for any family of finite groups that is closed under subquotients up to isomorphism. The rhetorical p-biset functors almost coincide with the rational p-biset functors. We show that, over a field with characteristic zero, the rhetorical biset functors are semisimple and, furthermore, they admit a character theory involving primitive characters of automorphism groups of cyclic groups.     

Recollements and homological dimensions

We investigate the behavior of the homological dimensions under recollements of derived categories of algebras. In particular, we establish a series of new bounds among the self-injective dimensions or ?-dimensions of the algebras linked by recollements of derived module categories.     

Gorensteinness,homological invariants and Gorenstein derived categories

Relations between Gorenstein derived categories, Gorenstein defect categories and Gorenstein stable categories are established. Using these, the Gorensteinness of an algebra A and invariants with respect to recollements of the bounded Gorenstein derived category D _gp ^b (A-mod) of A are investigated. Specifically, the Gorensteinness of A is characterized in terms of recollements of D _gp ^b (A-mod) and Gorenstein derived equivalences. It is also shown that Cohen-Macaulay-finiteness is invariant with respect to the recollements of D _gp ^b (A-mod).     

Algebraic linkage and homological algebra

Ricerche di Matematica - We prove that some of the main results of linkage theory can be extended to a more general context in homological algebra. Our main result states that, under suitable...     

Flag bundles,Chern classes and natural lifts

Summary The (total) Chern class of any incomplete flag bundle is determined, thus generalising those found for the complete flag bundle in [3] and for the projective bundle in [1, I] and [6]. We also generalise a formula of D. B. Scott in [4] to any incomplete flag bundle. Entrata in Redazione il 7 settembre 1976.     

Triangulated Spheres and Colored Cliques

Abstract. In [1] a generalization of Hall's theorem was proved for families of hypergraphs. The proof used Sperner's lemma. In [5] Meshulam proved an extension of this result, using homology and the nerve theorem. In this paper we show how the triangulations method can be used to derive Meshulam's results. As in [1], the proof is based on results on extensions of triangulations from the sphere to the full ball. A typical result of this type is that any triangulation of the (d-1) -dimensional sphere S ^d-1 can be extended to a triangulation of the ball B ^d , by adding one point at a time, having degree at most 2d to its predecessors.     

Finite-product-preserving functors,Kan extensions,and strongly-finitary 2-monads

We study those 2-monads on the 2-categoryCat of categories which, as endofunctors, are the left Kan extensions of their restrictions to the sub-2-category of finite discrete categories, describing their algebras syntactically. Showing that endofunctors of this kind are closed under composition involves a lemma on left Kan extensions along a coproduct-preserving functor in the context of cartesian closed categories, which is closely related to an earlier result of Borceux and Day.The first author gratefully acknowledges the support of the Australian Research Council.