Quasi-Projective and Formal-Analytic Arithmetic Surfaces
-
- Hardcover
- Taschenbuch ausgewählt
- eBook
-
Sprache:Englisch
73,99 €
inkl. gesetzl. MwSt.,
Beschreibung
Produktdetails
Einband
Taschenbuch
Erscheinungsdatum
04.08.2026
Verlag
University PressesSeitenzahl
264
Maße (L/B)
23,5/15,6 cm
Sprache
Englisch
ISBN
978-0-691-28788-1
A milestone in the geometric understanding of algebraization theorems that also provides an introduction to Arakelov geometry
Motivated 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.
Kundinnen und Kunden meinen
Verfassen Sie die erste Bewertung zu diesem Artikel
Helfen Sie anderen Kund*innen durch Ihre Meinung
Kurze Frage zu unserer Seite
Vielen Dank für Ihr Feedback
Wir nutzen Ihr Feedback, um unsere Produktseiten zu verbessern. Bitte haben Sie Verständnis, dass wir Ihnen keine Rückmeldung geben können. Falls Sie Kontakt mit uns aufnehmen möchten, können Sie sich aber gerne an unseren Kund*innenservice wenden.
zum Kundenservice