THE GEOMETRY OF FROBENIOIDS I: THE GENERAL THEORY

• MOCHIZUKI Shinichi

  Research Institute for Mathematical Sciences Kyoto University

抄録

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.

収録刊行物

• 九州数学雑誌

  九州数学雑誌 62 (2), 293-400, 2008

  九州大学大学院数理学研究院

キーワード

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

詳細情報

• CRID: 1390282680205040640
• NII論文ID: 130000063241
• NII書誌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
• 本文言語コード: en
• データソース種別:
  • JaLC
  • Crossref
  • CiNii Articles
  • KAKEN
• 抄録ライセンスフラグ: 使用不可