Capacity theory on algebraic curves and canonical heights

Robert Rumely

Groupe de travail d'analyse ultramétrique (1984-1985)

  • Volume: 12, Issue: 2, page 1-17

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Rumely, Robert. "Capacity theory on algebraic curves and canonical heights." Groupe de travail d'analyse ultramétrique 12.2 (1984-1985): 1-17. <http://eudml.org/doc/91944>.

@article{Rumely1984-1985,
author = {Rumely, Robert},
journal = {Groupe de travail d'analyse ultramétrique},
keywords = {canonical heights; Fekete-Szegö theorem; the logarithmic capacity; Galois orbits},
language = {eng},
number = {2},
pages = {1-17},
publisher = {Secrétariat mathématique},
title = {Capacity theory on algebraic curves and canonical heights},
url = {http://eudml.org/doc/91944},
volume = {12},
year = {1984-1985},
}

TY - JOUR
AU - Rumely, Robert
TI - Capacity theory on algebraic curves and canonical heights
JO - Groupe de travail d'analyse ultramétrique
PY - 1984-1985
PB - Secrétariat mathématique
VL - 12
IS - 2
SP - 1
EP - 17
LA - eng
KW - canonical heights; Fekete-Szegö theorem; the logarithmic capacity; Galois orbits
UR - http://eudml.org/doc/91944
ER -

References

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  1. [Ar] Arakelov ( S. ) . - Intersection theory for divisors on an arithmetic surface [in Russian], Izvest. Akad. Nauk SSSR, Serija mat., t. 38, 1974, p. 1179- 1192. Zbl0355.14002MR472815
  2. [C] Cantor ( D.). - On an extension of the definition of transfinite dianeter and some applications, J. für reine und angew. Math., t. 316, 1980, p. 160- 207. Zbl0445.30019MR581330
  3. [F-S] Fekete ( M.) and Szegö ( G. ). - On algebraic equations with integral coefficients whose roots belong to a given point set, Math. Z., t. 63, 1955/56, p. 158-172. Zbl0066.27002MR72941
  4. [Gr] Gross ( B.). - Local heights on curves (to appear). Zbl0605.14027MR861983
  5. [Gr-Z] Gross ( B.) and Zagier ( D. ). - The Green's function for curves uniformized by the upper half plane (to appear). 
  6. [Kan] Kani ( E. ). - Weil heights, Néron pairings and v-metrics on curves (to appear). Zbl0594.14023MR823255
  7. [L] Lang ( S.). - Elliptic curves, diophantine analysis. - Berlin, Springer-Verlag, 1978 (Grundlehren der mathematischen Wissenschaften, 231). Zbl0388.10001MR518817
  8. [M] Manin ( Yu.). - The refined structure of the Néron-Tate height [in Russian] Mat. Sbornik, t. 83, 1970, p. 331-348 ; [in English] Math. USSR-Sbornik, t. 12, 1970, p. 325-342. Zbl0252.14007MR276245
  9. [N] Néron ( A.). - Quasi-fonctions et hauteurs sur les variétés abéliennes, Annals of Math., Series 2, t. 82, 1965, p. 249-331. Zbl0163.15205MR179173
  10. [R] Rumely ( R.). - Capacity theory on algebraic curves (nanuscript). 
  11. [Ts] Tsuji ( M.). - Potential theory in modern function theory. - Tokyo, New York, Maruzen Comp., 1959 ; reprinted 2nd edition : New York, Chelsea, 1975. Zbl0087.28401MR114894

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