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II - Sheaves of Monoids

Published online by Cambridge University Press:  02 November 2018

Arthur Ogus
Arthur Ogus
Affiliation:
University of California, Berkeley
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Summary

Chapter II is devoted to the study of sheaves of monoids on a topological space.It includes the definition and basic constructions of monoschemes,which are generalizations of the fans classically used to construct toric varieties. Quasi-coherent sheaves of sets on monoschemese are defined, as well asprojective, proper, and separated morphisms of monoschemes.In particularit is shown how morphisms of monoschemes can be exactified by a monoidal transformation. Also discussed arethe key concepts of charts and coherence for a sheaf of monoids.

Keywords

monoidal spacesmonoschemesfansmonoidal transformationsmoment mapcharts and coherenceneat chartsrelatively coherent sheaf of faces
Type
Chapter
Information
Lectures on Logarithmic Algebraic Geometry , pp. 184 - 269
Publisher: Cambridge University Press
Print publication year: 2018

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  • Sheaves of Monoids
  • Arthur Ogus, University of California, Berkeley
  • Book: Lectures on Logarithmic Algebraic Geometry
  • Online publication: 02 November 2018
  • Chapter DOI: https://doi.org/10.1017/9781316941614.003
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  • Sheaves of Monoids
  • Arthur Ogus, University of California, Berkeley
  • Book: Lectures on Logarithmic Algebraic Geometry
  • Online publication: 02 November 2018
  • Chapter DOI: https://doi.org/10.1017/9781316941614.003
Available formats
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Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Sheaves of Monoids
  • Arthur Ogus, University of California, Berkeley
  • Book: Lectures on Logarithmic Algebraic Geometry
  • Online publication: 02 November 2018
  • Chapter DOI: https://doi.org/10.1017/9781316941614.003
Available formats
×