Lectures on the Arithmetic Riemann-Roch Theorem. (AM-127), Volume 127 / / Gerd Faltings
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| Autore: |
Faltings Gerd
|
| Titolo: |
Lectures on the Arithmetic Riemann-Roch Theorem. (AM-127), Volume 127 / / Gerd Faltings
|
| Pubblicazione: | Princeton, NJ : , : Princeton University Press, , [2016] |
| ©1992 | |
| Descrizione fisica: | 1 online resource (113 pages) |
| Disciplina: | 516.3/5 |
| Soggetto topico: | Geometry, Algebraic |
| Riemann-Roch theorems | |
| Soggetto non controllato: | Addition |
| Adjoint | |
| Alexander Grothendieck | |
| Algebraic geometry | |
| Analytic torsion | |
| Arakelov theory | |
| Asymptote | |
| Asymptotic expansion | |
| Asymptotic formula | |
| Big O notation | |
| Cartesian coordinate system | |
| Characteristic class | |
| Chern class | |
| Chow group | |
| Closed immersion | |
| Codimension | |
| Coherent sheaf | |
| Cohomology | |
| Combination | |
| Commutator | |
| Computation | |
| Covariant derivative | |
| Curvature | |
| Derivative | |
| Determinant | |
| Diagonal | |
| Differentiable manifold | |
| Differential form | |
| Dimension (vector space) | |
| Divisor | |
| Domain of a function | |
| Dual basis | |
| E6 (mathematics) | |
| Eigenvalues and eigenvectors | |
| Embedding | |
| Endomorphism | |
| Exact sequence | |
| Exponential function | |
| Generic point | |
| Heat kernel | |
| Injective function | |
| Intersection theory | |
| K-group | |
| Levi-Civita connection | |
| Line bundle | |
| Linear algebra | |
| Local coordinates | |
| Mathematical induction | |
| Morphism | |
| Natural number | |
| Neighbourhood (mathematics) | |
| Parameter | |
| Projective space | |
| Pullback (category theory) | |
| Pullback (differential geometry) | |
| Pullback | |
| Riemannian manifold | |
| Riemann–Roch theorem | |
| Self-adjoint operator | |
| Smoothness | |
| Sobolev space | |
| Stochastic calculus | |
| Summation | |
| Supertrace | |
| Theorem | |
| Transition function | |
| Upper half-plane | |
| Vector bundle | |
| Volume form | |
| Altri autori: |
ZhangShouwu
|
| Nota di bibliografia: | Includes bibliographical references. |
| Nota di contenuto: | Frontmatter -- TABLE OF CONTENTS -- INTRODUCTION -- LIST OF SYMBOLS -- LECTURE 1. CLASSICAL RIEMANN-ROCH THEOREM -- LECTURE 2. CHERN CLASSES OF ARITHMETIC VECTOR BUNDLES -- LECTURE 3. LAPLACIANS AND HEAT KERNELS -- LECTURE 4. THE LOCAL INDEX THEOREM FOR DIRAC OPERATORS -- LECTURE 5. NUMBER OPERATORS AND DIRECT IMAGES -- LECTURE 6. ARITHMETIC RIEMANN-ROCH THEOREM -- LECTURE 7. THE THEOREM OF BISMUT-VASSEROT -- REFERENCES |
| Sommario/riassunto: | 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. |
| Titolo autorizzato: | Lectures on the Arithmetic Riemann-Roch Theorem. (AM-127), Volume 127 |
| ISBN: | 1-4008-8247-8 |
| Formato: | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione: | Inglese |
| Record Nr.: | 9910154744103321 |
| Lo trovi qui: | Univ. Federico II |
| Opac: | Controlla la disponibilità qui |
Serie:
Annals of mathematics studies ; ; no. 127.