English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

Let p be a fixed prime and let K be an unstable algebra over the mod-p Steenrod algebra A such that K is finitely generated s graded Fp-algebra. Let Kfg — ̂ tt denote the abelian category of finitely generated ΑΓ-modules with a compatible unstable ^4-module structure. We study various concepts of commutative algebra in this setting. The r le of the prime ideal spectrum of a commutative ring is here taken by a category 0t (K) which, roughly speaking, consists of the ,4-invariant prime ideals of ^together with certain "Galois Information"; sheaves will correspond to functors on this category, and the role of the sheaf associated to a module will be taken by the components of Lannes' Γ-functor. We discuss the notions of support, of α-torsion modules (for an invariant ideal α of K) and of localization away from the Serre subcategory ̂ rs(a) of α-torsion modules in our setting. We show that the category Kfg — <% has enough injectives and use these injectives to study these localizations and their derived functors; they are closely related to the derived functors of the α-torsion functor Fa. Our results are formally analogous to Grothendieck's results in the classical Situation of modules over a noetherian commutative ring R [Gr]. Important for applications is the case K = H* BG, the mod-p cohomology of a classifying space of a compact Lie group (or a suitable discrete group), and M = H%X where Xis a (suitable) G-CPF-complex. In these cases the category $(K) and the functor on ? (K) associated to H^X can be described in terms of group theoretic and geometric data, and our theory yields a far-reaching generalization of a result of Jackowski and McClure [JM] resp. of Dwyer and Wilkerson [DW 2]. As a concrete application of our theory we describe the size of the kernel of the restriction map from the unknown mod-2 cohomology of the S-arithmetic group GL(n, Z[1/2]) to the known cohomology of its subgroup Dn of diagonal matrices. 13a Journal f r Mathematik. Band 478 190 Henn, Commutative algebra of unstable K-modules

Commutative algebra of unstable K-modules, Lannes' T-functor and equivariant mod-p cohomology.