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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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. MathOverflow works best with JavaScript enabled.

Learning Arakelov geometry Ask Question. This page was last edited on 28 Mayat 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. The exposition stands out of its high degree of clarity, 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.

There are definitely situations outside Arakelov geometry where analytic torsion appears. The arithmetic Riemann—Roch theorem is similar except that the Todd class gets multiplied by a certain power series. Thanks for the answer. Ariyan Javanpeykar 5, 1 22 The arithmetic Riemann—Roch theorem states.


Arakelov geometry in nLab

Home Questions Tags Users Unanswered. This is a timely monograph that should appeal to researchers in this important area of mathematics.

I have a complex gsometry background Griffiths and Harris, Huybrechts, Demailley etc. Online Price 1 Label: I only know that analytic araeklov appears in Arakelov geometry when one wants to define the Quillen metric on the determinant of cohomology of a hermitian line bundle.

Join our email list. See our librarian page for additional eBook ordering options. 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. Bruin’s master’s thesis written under the supervision of R.

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This is where schemes and number theory come into play.

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. 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. Email Required, but never shown.


I think the “road to Arakelov geometry” for someone from analysis is a bit different, but I’m convinced that the following is a good way to start for everyone. 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.

Algebraic geometry Diophantine geometry. Arakelov Geometry Share this page. Post as a guest Name. In addition, the author presents, with full details, the proof of Faltings’ Riemann—Roch theorem.

Mathematics > Algebraic Geometry

Sign up using Email and Password. Also, I understand some PDE. Ordering on the AMS Bookstore is limited to individuals for personal use only.

In mathematicsArakelov theory or Arakelov geometry is an approach to Diophantine geometrynamed for Suren Arakelov.