Kyushu Journal of Mathematics
THE GEOMETRY OF FROBENIOIDS I: THE GENERAL THEORY
Shinichi MOCHIZUKI
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Volume 62 (2008) Issue 2 Pages 293-400

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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.

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© 2008 by Faculty of Mathematics, Kyushu University
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