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Книга Quasi–Projective and Formal–Analytic Arithmetic Surfaces Jean–benoît Bost

Quasi–Projective and Formal–Analytic Arithmetic Surfaces

Автор: Jean–benoît Bost, François Charles
Език: Английски език
Корици: С меки корици
Издател: Princeton University Press
Наличност: Очакван нов продукт
Издание 04. 08. 2026
78.08 € 152.72 лв
A milestone in the geometric understanding of algebraization theorems that also provides an introduc...

Информация за книгата

Автор
Jean–benoît Bost, François Charles
Език
Английски език
Корици
Книга - С меки корици
Издадена
2026
страници
288
EAN
9780691287881
ISBN
0691287880
Enbook ID
50894793
Издател
Princeton University Press
Теглоt
666
Размери
155 x 234 x 15

Пълно описание

A milestone in the geometric understanding of algebraization theorems that also provides an introduction to Arakelov geometryMotivated by questions of transcendental number theory, arithmetic, and Diophantine geometry, this book provides a thorough study of a new kind of mathematical object—formal-analytic arithmetic surfaces. These are arithmetic counterparts in Arakelov geometry of germs of complex surfaces along projective complex curves. Formal-analytic arithmetic surfaces involve both an arithmetic and a complex-analytic aspect, and they provide a natural framework for old and new arithmetic algebraization theorems. Formal-analytic arithmetic surfaces admit a rich geometry that parallels the geometry of complex analytic surfaces. Notably the dichotomy between pseudoconvexity and pseudoconcavity plays a central role in this framework. The book develops the general theory of formal-analytic arithmetic surfaces, making notable use of real invariants coming from an infinite-dimensional version of geometry of numbers. Those so-called theta invariants play the role of the dimension of spaces of sections of vector bundles in complex geometry. Relating those invariants to the classical invariants of Arakelov intersection theory involves a new real invariant attached to certain maps between Riemann surfaces, the Archimedean overflow, which is introduced and discussed in detail. The book contains applications to concrete Diophantine problems. It provides a generalization of the arithmetic holonomicity theorem of Calegari-Dimitrov-Tang regarding the dimension of spaces of power series with integral coefficients satisfying some convergence conditions. It also establishes new effective finiteness theorems for fundamental groups of arithmetic surfaces. Along the way, the book discusses many tools, classical and new, in Arakelov geometry and complex analysis, and it can be used as an introduction to some of these topics.

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