The algebraic chromatic splitting conjecture for Noetherian ring spectra

Finite Correspondence of Spectra in Noetherian Ring Extensions

Let R <-* S be an embedding of associative noetherian rings such that 5 is finitely generated as a right Ä-module. There is a correspondence from the prime spectrum of S to the prime spectrum of R obtained by associating to a given prime ideal P of S the prime ideals of R minimal over P n R . The prime and primitive ideal theories for several specific noncommutative noetherian rings, including ...

Bousfield Localization Functors and Hopkins’ Chromatic Splitting Conjecture

This paper arose from attempting to understand Bousfield localization functors in stable homotopy theory. All spectra will be p-local for a prime p throughout this paper. Recall that if E is a spectrum, a spectrum X is E-acyclic if E ∧X is null. A spectrum is E-local if every map from an E-acyclic spectrum to it is null. A map X → Y is an E-equivalence if it induces an isomorphism on E∗, or equ...

Chromatic Splitting

Go-spaces and Noetherian Spectra

The Noetherian type of a space is the least κ for which the space has a κop-like base, i.e., a base in which no element has κ-many supersets. We prove some results about Noetherian types of (generalized) ordered spaces and products thereof. For example: the density of a product of not-too-many compact linear orders never exceeds its Noetherian type, with equality possible only for singular Noet...

The Splitting Subspace Conjecture

We answer a question by Niederreiter concerning the enumeration of a class of subspaces of finite dimensional vector spaces over finite fields by proving a conjecture by Ghorpade and Ram.