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.
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.
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.
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The arithmetic Riemann—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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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.