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46
Morava Ktheories and localisation
 MEM. AMER. MATH. SOC
, 1999
"... We study the structure of the categories of K(n)local and E(n)local spectra, using the axiomatic framework developed in earlier work of the authors with John Palmieri. We classify localising and colocalising subcategories, and give characterisations of small, dualisable, and K(n)nilpotent spectra ..."
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Cited by 105 (19 self)
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We study the structure of the categories of K(n)local and E(n)local spectra, using the axiomatic framework developed in earlier work of the authors with John Palmieri. We classify localising and colocalising subcategories, and give characterisations of small, dualisable, and K(n)nilpotent spectra. We give a number of useful extensions to the theory of vn self maps of finite spectra, and to the theory of Landweber exactness. We show that certain rings of cohomology operations are left Noetherian, and deduce some powerful finiteness results. We study the Picard group of invertible K(n)local spectra, and the problem of grading homotopy groups over it. We prove (as announced by Hopkins and Gross) that the BrownComenetz dual of MnS lies in the Picard group. We give a detailed analysis of some examples when n =1 or 2, and a list of open problems.
The stack of formal groups in stable homotopy theory
 Adv. Math
"... We construct the algebraic stack of formal groups and use it to provide a new perspective onto a recent result of M. Hovey and N. Strickland on comodule categories for Landweber exact algebras. This leads to a geometric understanding of their results as well as to a generalisation. 1. ..."
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Cited by 25 (4 self)
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We construct the algebraic stack of formal groups and use it to provide a new perspective onto a recent result of M. Hovey and N. Strickland on comodule categories for Landweber exact algebras. This leads to a geometric understanding of their results as well as to a generalisation. 1.
Additivity for derivator Ktheory
, 2008
"... We prove the additivity theorem for the Ktheory of triangulated derivators. This solves one of the conjec ..."
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Cited by 17 (0 self)
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We prove the additivity theorem for the Ktheory of triangulated derivators. This solves one of the conjec
Quasicoherent sheaves on the moduli stack of formal groups
"... For years I have been echoing my betters, especially Mike Hopkins, and telling anyone who would listen that the chromatic picture of stable homotopy theory is dictated and controlled by the geometry of the moduli stack Mfg of smooth, onedimensional formal groups. Specifically, I would say that the ..."
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Cited by 10 (1 self)
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For years I have been echoing my betters, especially Mike Hopkins, and telling anyone who would listen that the chromatic picture of stable homotopy theory is dictated and controlled by the geometry of the moduli stack Mfg of smooth, onedimensional formal groups. Specifically, I would say that the height filtration of Mfg dictates a canonical and natural decomposition of a quasicoherent sheaf on Mfg, and this decomposition predicts and controls the chromatic decomposition of a finite spectrum. This sounds well, and is even true, but there is no single place in the literature where I could send anyone in order for him or her to get a clear, detailed, unified, and linear rendition of this story. This document is an attempt to set that right. Before going on to state in detail what I actually hope to accomplish here, I should quickly acknowledge that the opening sentences of this introduction and, indeed, this whole point of view is not original with me. I have already mentioned Mike Hopkins, and just about everything I’m going to say here is encapsulated in the table in section 2 of [15] and can be gleaned from the notes
Heller triangulated categories
, 2007
"... complexes with entries in E. Shifting a complex by 3 positions yields an outer shift ..."
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Cited by 6 (0 self)
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complexes with entries in E. Shifting a complex by 3 positions yields an outer shift
Systems of diagram categories and Ktheory I
, 2004
"... To any left system of diagram categories or to any left pointed dérivateur a Ktheory space is associated. This Ktheory space is shown to be canonically an infinite loop space and to have a lot of common properties with Waldhausen’s Ktheory. A weaker version of additivity is shown. Also, Quillen ..."
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Cited by 5 (1 self)
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To any left system of diagram categories or to any left pointed dérivateur a Ktheory space is associated. This Ktheory space is shown to be canonically an infinite loop space and to have a lot of common properties with Waldhausen’s Ktheory. A weaker version of additivity is shown. Also, Quillen’s Ktheory of a large class of exact categories including the abelian categories is