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Axiomatic, Enriched and Motivic Homotopy Theory

Proceedings of the NATO Advanced Study Institute on Axiomatic, Enriched and Motivic Homotopy Theory Cambridge, United Kingdom 9–20 September 2002

  • Conference proceedings
  • © 2004

Overview

Editors:
  1. J. P. C. Greenlees

    1. University of Sheffield, UK

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Part of the book series: NATO Science Series II: Mathematics, Physics and Chemistry (NAII, volume 131)

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Table of contents (10 papers)

  1. Front Matter

    Pages i-xi
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  2. General Surveys

    1. Front Matter

      Pages 1-1
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    2. Localizations

      • W. G. Dwyer
      Pages 3-28

    3. Generalised Sheaf Cohomology Theories

      • J. F. Jardine
      Pages 29-68

    4. Axiomatic Stable Homotopy

      • N. P. Strickland
      Pages 69-98

  3. Special Surveys

    1. Front Matter

      Pages 99-99
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    2. (PRE-)Sheaves of Ring Spectra Over the Moduli Stack of Formal Group Laws

      • Paul G. Goerss
      Pages 101-131

    3. Operads and Cosimplicial Objects: An Introduction

      • James E. McClure, Jeffrey H. Smith
      Pages 133-171

    4. From Hag To Dag: Derived Moduli Stacks

      • Bertrand Toën, Gabriele Vezzosi
      Pages 173-216

  4. Motivic Homotopy Theory

    1. Front Matter

      Pages 217-217
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    2. On the Motivic π0 of the Sphere Spectrum

      • Fabien Morel
      Pages 219-260

    3. Riemann-Roch Theorems for Oriented Cohomology

      • I. Panin, A. Smirnov
      Pages 261-333

    4. Equivariant Motivic Phenomena

      • Victor Snaith
      Pages 335-383

    5. A Road Map of Motivic Homotopy and Homology Theory

      • Charles Weibel
      Pages 385-392
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Keywords

About this book

The NATO Advanced Study Institute "Axiomatic, enriched and rna­ tivic homotopy theory" took place at the Isaac Newton Institute of Mathematical Sciences, Cambridge, England during 9-20 September 2002. The Directors were J.P.C.Greenlees and I.Zhukov; the other or­ ganizers were P.G.Goerss, F.Morel, J.F.Jardine and V.P.Snaith. The title describes the content well, and both the event and the contents of the present volume reflect recent remarkable successes in model categor­ ies, structured ring spectra and homotopy theory of algebraic geometry. The ASI took the form of a series of 15 minicourses and a few extra lectures, and was designed to provide background, and to bring the par­ ticipants up to date with developments. The present volume is based on a number of the lectures given during the workshop. The ASI was the opening workshop of the four month programme "New Contexts for Stable Homotopy Theory" which explored several themes in greater depth. I am grateful to the Isaac Newton Institute for providing such an ideal venue, the NATO Science Committee for their funding, and to all the speakers at the conference, whether or not they were able to contribute to the present volume. All contributions were refereed, and I thank the authors and referees for their efforts to fit in with the tight schedule. Finally, I would like to thank my coorganizers and all the staff at the Institute for making the ASI run so smoothly. J.P.C.GREENLEES.

Editors and Affiliations

  • University of Sheffield, UK

    J. P. C. Greenlees

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