Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Search

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

1 results

  • III - Logarithmic Schemes

  • Arthur Ogus, University of California, Berkeley
  • Book:
    Lectures on Logarithmic Algebraic Geometry
    Published online:
    02 November 2018
    Print publication:
    08 November 2018, pp 270-360

  • Summary

    Chapter III introduces log geometry per se, beginning with the definitions of log structures and log schemes and their charts.It discusses both étale and Zariski log structuresand describes basic examples, including log points and log dashes and the log schemes arising from divisors with normal crossings and semistable reduction.So-called “compactifying” log structures are especially important, and conditions are given for such structures to be coherent or relatively coherent.Also discussed are hollow, solid, and regular log structures. The second part of Chapter II is devoted to morphisms of log schemes.It begins with the construction of fiber products, which is delicate in the category of fine log schemes.Then it discusses special classes of morphisms, including exact, integral, and saturated morphisms, as well as immersions, small morphisms, inseparable morphisms, and Frobenius.It concludes with a definition and brief discussion of log blowups and their functorial properties.