THE GEOMETRY OF FROBENIOIDS I: THE GENERAL THEORY

• MOCHIZUKI Shinichi

  Research Institute for Mathematical Sciences Kyoto University

Abstract

We develop the theory of Frobenioids, which may be regarded as a category-theoretic abstraction of the theory of divisors and line bundles on models of finite separable extensions of a given function field or number field. This sort of abstraction is analogous to the role of Galois categories in Galo is theory or monoids in the geometry of log schemes. This abstract category-theoretic framework preserves many o f the important features of the classical theory of divisors and line bundles on models of finite separable extensions of a function field or number field such as the global degree of an arithmetic line bundle over a number field, but also exhibits interesting new phenomena, such as a ‘Frobenius endomorphism’ of the Frobenioid associated to a number field.

Journal

• Kyushu Journal of Mathematics

  Kyushu Journal of Mathematics 62 (2), 293-400, 2008

  Faculty of Mathematics, Kyushu University

Keywords

• categories
• Galois categories
• Frobenius
• monoids
• log schemes

Details

• CRID: 1390282680205040640
• NII Article ID: 130000063241
• NII Book ID: AA10994346
• DOI: 10.2206/kyushujm.62.293
• ISSN: 18832032
• ISSN: 13406116
• Web Site: https://www.jstage.jst.go.jp/article/kyushujm/62/2/62_2_293/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed