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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

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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
×