Lectures On The Arithmetic Riemann Roch Theorem
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Lectures on the Arithmetic Riemann Roch Theorem
Author | : Gerd Faltings |
Publsiher | : Princeton University Press |
Total Pages | : 112 |
Release | : 1992-03-10 |
Genre | : Mathematics |
ISBN | : 9780691025445 |
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The arithmetic Riemann-Roch Theorem has been shown recently by Bismut-Gillet-Soul. The proof mixes algebra, arithmetic, and analysis. The purpose of this book is to give a concise introduction to the necessary techniques, and to present a simplified and extended version of the proof. It should enable mathematicians with a background in arithmetic algebraic geometry to understand some basic techniques in the rapidly evolving field of Arakelov-theory.
Lectures on the Arithmetic Riemann Roch Theorem
Author | : Gerd Faltings |
Publsiher | : Unknown |
Total Pages | : 100 |
Release | : 1992 |
Genre | : Geometry, Algebraic |
ISBN | : 0691087717 |
Download Lectures on the Arithmetic Riemann Roch Theorem Book in PDF, Epub and Kindle
The arithmetic Riemann-Roch Theorem has been shown recently by Bismut-Gillet-Soul. The proof mixes algebra, arithmetic, and analysis. The purpose of this book is to give a concise introduction to the necessary techniques, and to present a simplified and extended version of the proof. It should enable mathematicians with a background in arithmetic algebraic geometry to understand some basic techniques in the rapidly evolving field of Arakelov-theory.
Lectures on the Arithmetic Riemann Roch Theorem AM 127 Volume 127
Author | : Gerd Faltings |
Publsiher | : Princeton University Press |
Total Pages | : 118 |
Release | : 2016-03-02 |
Genre | : Mathematics |
ISBN | : 9781400882472 |
Download Lectures on the Arithmetic Riemann Roch Theorem AM 127 Volume 127 Book in PDF, Epub and Kindle
The arithmetic Riemann-Roch Theorem has been shown recently by Bismut-Gillet-Soul. The proof mixes algebra, arithmetic, and analysis. The purpose of this book is to give a concise introduction to the necessary techniques, and to present a simplified and extended version of the proof. It should enable mathematicians with a background in arithmetic algebraic geometry to understand some basic techniques in the rapidly evolving field of Arakelov-theory.
An Arithmetic Riemann Roch Theorem for Singular Arithmetic Surfaces
Author | : Wayne Aitken |
Publsiher | : Unknown |
Total Pages | : 174 |
Release | : 1996 |
Genre | : Arithmetical algebraic geometry |
ISBN | : 1470401584 |
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Lectures on the Theory of Algebraic Functions of One Variable
Author | : Max Deuring |
Publsiher | : Springer |
Total Pages | : 157 |
Release | : 2006-11-15 |
Genre | : Mathematics |
ISBN | : 9783540383680 |
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An Arithmetic Riemann Roch Theorem for Singular Arithmetic Surfaces
Author | : Wayne Aitken |
Publsiher | : American Mathematical Soc. |
Total Pages | : 174 |
Release | : 1996 |
Genre | : Mathematics |
ISBN | : 9780821804070 |
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The first half of this work gives a treatment of Deligne's functorial intersection theory tailored to the needs of this paper. This treatment is intended to satisfy three requirements: 1) that it be general enough to handle families of singular curves, 2) that it be reasonably self-contained, and 3) that the constructions given be readily adaptable to the process of adding norms and metrics such as is done in the second half of the paper. The second half of the work is devoted to developing a class of intersection functions for singular curves that behaves analogously to the canonical Green's functions introduced by Arakelov for smooth curves. These functions are called intersection functions since they give a measure of intersection over the infinite places of a number field. The intersection over finite places can be defined in terms of the standard apparatus of algebraic geometry. Finally, the author defines an intersection theory for arithmetic surfaces that includes a large class of singular arithmetic surfaces. This culminates in a proof of the arithmetic Riemann-Roch theorem.
Lectures on Algebraic Geometry II
Author | : Günter Harder |
Publsiher | : Springer Science & Business Media |
Total Pages | : 376 |
Release | : 2011-04-21 |
Genre | : Mathematics |
ISBN | : 9783834881595 |
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This second volume introduces the concept of shemes, reviews some commutative algebra and introduces projective schemes. The finiteness theorem for coherent sheaves is proved, here again the techniques of homological algebra and sheaf cohomology are needed. In the last two chapters, projective curves over an arbitrary ground field are discussed, the theory of Jacobians is developed, and the existence of the Picard scheme is proved. Finally, the author gives some outlook into further developments- for instance étale cohomology- and states some fundamental theorems.
An Arithmetic Riemann Roch Theorem for Metrics with Cusps
Author | : Tobias Hahn |
Publsiher | : Unknown |
Total Pages | : 103 |
Release | : 2009 |
Genre | : Electronic Book |
ISBN | : 3832282319 |
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