# ARAKELOV GEOMETRY PDF

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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Thanks for the answer.

### Arakelov geometry in nLab

There is this arqkelov text by Demailly which motivates the treatment of intersection theory on the infinite fibers and probably suits you with your background. Publication Month and Year: Arakelov Geometry Share this page.

Since you don’t want to apply the analysis to do intersection theory on an arithmetic surface, you don’t have to go into this, I believe. Taking another look at that answer, it seems that my answer is written for people with a more algebraic background.

## Arakelov Geometry

By using this site, you agree to the Terms of Use and Privacy Policy. I have a complex analytic background Griffiths and Harris, Huybrechts, Demailley etc. Retrieved from ” https: I just don’t know any of them.

Now, I think after reading the relevant parts in the above references, you could start reading papers about analytic torsion assuming you’re already familiar with what this is.

Online Price 1 Label: This page was last edited on 28 Mayat Print Price 2 Label: Arakelov geometry studies a scheme X over the ring of integers Zby putting Hermitian metrics on holomorphic vector bundles over X Cthe complex points of X.

MathOverflow works best with JavaScript enabled. With this in mind the analytic part of the above gfometry should be ok to read. Prerequisites for reading this book are the basic results of algebraic geometry and the language of schemes.

### Arakelov Geometry

I only know that analytic torsion appears in Arakelov geometry when one wants to define the Quillen metric on the determinant of cohomology of a hermitian line bundle.

From Wikipedia, the free encyclopedia. Print Price 3 Label: Ordering on the AMS Bookstore is limited to individuals for personal use only.

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## Arakelov theory

The arithmetic Riemannâ€”Roch theorem states. 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. I would say Fulton’s book is not necessary since you anyway do intersection theory via K-theory. Online Price 3 Label: Compared to the beometry books on Arakelov geometry, the current monograph is much more up-to-date, detailed, comprehensive, and self-contained.

This is explained arxkelov well in Chapter 1. For this one defines arithmetic Chow groups CH p X of an arithmetic variety Xand defines Chern classes for Hermitian vector bundles over X taking values in the arithmetic Chow groups.

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Sign up using Facebook. Kyoto University, Kyoto, Japan. I also want to know if there are any applications of Analytic torsion outside Arakelov geometry. I don’t how much of these is needed to learn this stuff. Join our email list. 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.

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Graduate students interested in Diophantine and Arakelov geometry. 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. Bruin’s master’s thesis written under the supervision of R.

Grometry Vamsi, A while ago I wrote my point of view on what “you should and shouldn’t read” before studying Arakelov geometry. See What should I read before reading about Arakelov theory? Sign up using Email and Password. Email Required, but never shown.