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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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soft question – Learning Arakelov geometry – MathOverflow

In this context Bost araeklov an arithmetic Hodge index theorem and uses this to obtain Lefschetz theorems for arithmetic surfaces. Prerequisites for reading this book are the basic results of algebraic geometry and the language of schemes. Kyoto University, Kyoto, Japan. Online Price 2 Label: In addition, the author presents, with full details, the proof of Faltings’ Riemann—Roch theorem.

Home Questions Tags Users Unanswered. The book includes such fundamental results as arithmetic Hilbert—Samuel formula, arithmetic Nakai—Moishezon criterion, arithmetic Bogomolov inequality, the existence of small sections, the continuity of arithmetic volume function, the Lang—Bogomolov conjecture and so on.


Dual Price 1 Label: Algebraic geometry Diophantine geometry. Arakelov Araelov Share this page. I only know that analytic torsion appears in Arakelov geometry when one wants to define the Quillen metric on the arakeloc of cohomology of a hermitian line bundle.

I know almost nothing of schemes or of number theory. By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Bruin’s master’s thesis written under the supervision of R.

Libraries and resellers, please contact cust-serv ams. You should know about schemes in general, and a good deal about K-theory and intersection theory in particular Fulton’s book alone will not suffice. The arithmetic Riemann—Roch theorem is similar except that the Todd class gets multiplied by a certain power series.

What should I read before reading about Arakelov theory? 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. Graduate students interested in Diophantine and Arakelov geometry. MathOverflow works best with JavaScript enabled. Many important results are presented for the first time in a book, such as the arithmetic Nakai-Moishezon criterion or the arithmetic Bogomolov inequality.

The arithmetic Riemann—Roch theorem states. This is explained very well in Chapter 1.

Mathematics > Algebraic Geometry

This is a timely monograph that should appeal to researchers in this important area of mathematics. Vamsi 1, 14 Compared to the earlier books on Arakelov geometry, the current monograph is much more geomdtry, detailed, comprehensive, and self-contained. From Wikipedia, the free encyclopedia.


If you’re more comfortable with analysis than algebraic geometry, I think a good idea would be to start with the analytic part of Arakelov geometry. A while ago I wrote my adakelov of view on what “you should and shouldn’t read” before studying Arakelov geometry.

Online Price 3 Label: Print Price 2 Label: Thanks for the answer. It is used to study Diophantine equations in higher dimensions. Sign up using Facebook. Also, I understand some PDE.

I don’t how much of these is needed to learn this stuff. After explaining classical results about the geometry of numbers, the author starts with Arakelov geometry for arithmetic curves, and continues with Arakelov geometry of arithmetic surfaces and higher-dimensional varieties.

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