Author | Lang, Serge. author |
---|---|
Title | Introduction to Arakelov Theory [electronic resource] / by Serge Lang |
Imprint | New York, NY : Springer New York : Imprint: Springer, 1988 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-1031-3 |
Descript | X, 187 p. online resource |
I Metrics and Chern Forms -- ยง1. Nรฉron Functions and Divisors -- ยง2. Metrics on Line Sheaves -- ยง3. The Chern Form of a Metric -- ยง4. Chern Forms in the Case of Riemann Surfaces -- II Greenโs Functions on Rlemann Surface -- ยง1. Greenโs Functions -- ยง2. The Canonical Greenโs Function -- ยง3. Some Formulas About the Greenโs Function -- ยง4. Colemanโs Proof for the Existence of Greenโs Function -- ยง5. The Greenโs Function on Elliptic Curves -- III Intersection on an Arithmetic Surface -- ยง1. The Chow Groups -- ยง2. Intersections -- ยง3. Fibral Intersections -- ยง4. Morphisms and Base Change -- ยง5. Nรฉron Symbols -- IV Hodge Index Theorem and the Adjunction Formula -- ยง1. Arakelov Divisors and Intersections -- ยง2. The Hodge Index Theorem -- ยง3. Metrized Line Sheaves and Intersections -- ยง4. The Canonical Sheaf and the Residue Theorem -- ยง5. Metrizations and Arakelovโs Adjunction Formula -- V The Faltings Reimann-Roch Theorem -- ยง1. Riemann-Roch on an Arithmetic Curve -- ยง2. Volume Exact Sequences -- ยง3. Faltings Riemann-Roch -- ยง4. An Application of Riemann-Roch -- ยง5. Semistability -- ยง6. Positivity of the Canonical Sheaf -- VI Faltings Volumes on Cohomology -- ยง1. Determinants -- ยง2. Determinant of Cohomology -- ยง3. Existence of the Faltings Volumes -- ยง4. Estimates for the Faltings Volumes -- ยง5. A Lower Bound for Greenโs Functions -- Appendix by Paul Vojta Diophantine Inequalities and Arakelov Theory -- ยง1. General Introductory Notions -- ยง2. Theorems over Function Fields -- ยง3. Conjectures over Number Fields -- ยง4. Another Height Inequality -- ยง5. Applications -- References -- Frequently Used Symbols