The analogy between number fields and function fields suggests to consider the scheme S = SpecoK as an affine smooth curve. The motto of Arakelov geometry. The main goal of this book is to present the so-called birational Arakelov geometry, which can be viewed as an arithmetic analog of the. Arakelov theory. A combination of the Grothendieck algebraic geometry of schemes over with Hermitian complex geometry on their set of.

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Arakelov Geometry

See What should I read before reading about Arakelov theory? Online Price 2 Label: There’s many of these, but I’m not the person to tell you which one is the best to start with.

Translations of Mathematical Monographs.

Join our email list. Post Your Answer Discard By clicking “Post Your Answer”, you acknowledge that you have read our updated terms of serviceprivacy policy and cookie policyand that your continued use of the website is subject to these policies. Dual Price 1 Label: Bruin’s master’s thesis written under the supervision of R. Ariyan Javanpeykar geoometry, 1 22 This is explained very well in Chapter 1.


Mathematics > Algebraic Geometry

Print Price 1 Label: The arithmetic Riemann—Roch theorem states. Geometey using our site, you acknowledge that you have read and understand egometry Cookie PolicyPrivacy Policyand our Terms of Service. There is this nice text by Demailly which motivates the treatment of intersection theory on the infinite fibers and probably suits you with your background.

MathOverflow works best with JavaScript enabled. Learning Arakelov geometry Ask Question. Views Read Edit View history. Libraries and resellers, please contact cust-serv ams. Prerequisites for reading this book are the basic results of algebraic geometry and the language of schemes.

Dual Price 2 Label: I have a complex analytic background Griffiths and Harris, Huybrechts, Demailley etc. Sign up using Email and Password. Online Price 3 Label: This is where schemes and number theory come into play.

I don’t how much of these is needed to learn this stuff. What should I read before reading about Arakelov theory?

Algebraic geometry Diophantine geometry. Sign up or log in Sign up using Google. I want to learn Arakelov geometry atleast till the point I can “apply” computations of Bott-Chern forms and Analytic torsion to producing theorems of interest in Arakelov geometry. Author s Product display: It is used to study Diophantine equations in higher dimensions.


The rich bibliography of seventy-eight references certainly serves as a useful guide to further reading with regard to the more recent research literature in the field. In addition, the author presents, with full details, the proof of Faltings’ Riemann—Roch theorem. Print Price 3 Label: The main goal of this book is to present the so-called birational Arakelov geometry, which can be viewed as an arithmetic analog of the classical birational geometry, i.

soft question – Learning Arakelov geometry – MathOverflow

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The arithmetic Riemann—Roch theorem then describes how the Chern class behaves under pushforward of vector bundles under a proper map of arithmetic varieties. The exposition stands out of its high degree of arkelov, completeness, rigor and topicality, which also makes the volume an excellent textbook on the subject for seasoned graduate students and young researchers in arithmetic algebraic geometry.