Bulletin of the American Mathematical Society

MathSciNet review: 1567972
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Book Information:

Author: Robert S. Rumely
Title: Capacity theory on algebraic curves
Additional book information: Lecture Notes in Mathematics, vol. 1378, Springer-Verlag, Berlin, Heidelberg, and New York, 1989, 437 pp., US$37.50. ISBN 3-540-51410-4.

David G. Cantor, On an extension of the definition of transfinite diameter and some applications, J. Reine Angew. Math. 316 (1980), 160–207. MR 581330, DOI 10.1515/crll.1980.316.160

Ted Chinburg, Capacity theory on varieties, Compositio Math. 80 (1991), no. 1, 75–84. MR 1127060

[3]

G. Faltings, The general case of S. Lang's Conjecture, preprint, 1991.

M. Fekete, Über die Verteilung der Wurzeln bei gewissen algebraischen Gleichungen mit ganzzahligen Koeffizienten, Math. Z. 17 (1923), no. 1, 228–249 (German). MR 1544613, DOI 10.1007/BF01504345

M. Fekete and G. Szegö, On algebraic equations with integral coefficients whose roots belong to a given point set, Math. Z. 63 (1955), 158–172. MR 72941, DOI 10.1007/BF01187931

Henri Gillet and Christophe Soulé, Arithmetic intersection theory, Inst. Hautes Études Sci. Publ. Math. 72 (1990), 93–174 (1991). MR 1087394

Ernst Kani, Potential theory on curves, Théorie des nombres (Quebec, PQ, 1987) de Gruyter, Berlin, 1989, pp. 475–543. MR 1024584

Robert Rumely, Capacity theory on algebraic curves and canonical heights, Study group on ultrametric analysis, 12th year, 1984/85, No. 2, Secrétariat Math., Paris, 1985, pp. Exp. No. 22, 17. MR 848999

[9]

-, On the relation between Cantor's capacity and Chinburg's sectional capacity, preprint (1990).

B. A. Taylor, Book Review: Capacities in complex analysis, Bull. Amer. Math. Soc. (N.S.) 24 (1991), no. 1, 213–216. MR 1567903, DOI 10.1090/S0273-0979-1991-15993-8

Paul Vojta, Siegel’s theorem in the compact case, Ann. of Math. (2) 133 (1991), no. 3, 509–548. MR 1109352, DOI 10.2307/2944318

Shouwu Zhang, Positive line bundles on arithmetic surfaces, Ann. of Math. (2) 136 (1992), no. 3, 569–587. MR 1189866, DOI 10.2307/2946601

[1]

D. Cantor, On an extension of the definition of transfinite diameter and some applications, J. Reine Angew. Math. 316 (1980), 160-207. MR 581330 (81m:12002)

[2]

T. Chinburg, Capacity theory on varieties, Compositio Math. 80 (1991), 75-84. MR 1127060 (93d:14039)

[3]

G. Faltings, The general case of S. Lang's Conjecture, preprint, 1991.

[4]

M. Fekete, Über die Verteilung der Wurzeln bei gewissen algebraischen Gleichungen mit ganzzahligen Koeffizienten, Math. Z. 17 (1923), 228-249. MR 1544613

[5]

M. Fekete and G. Szegö, On algebraic equations with integral coefficients whose roots belong to a given point set, Math. Z. 63 (1955), 158-172. MR 0072941 (17:355a)

[6]

H. Gillet and C. Soulé, Arithmetic intersection theory, Inst. Hautes Études Sci. Publ. Math. 72 (1990), 93-174. MR 1087394 (92d:14016)

[7]

E. Kani, Potential theory on curves, Proc. Internat. Conf. Number Theory, Quebec, 1987 (to appear). MR 1024584 (91e:14020)

[8]

R. Rumely, Capacity theory on algebraic curves and canonical heights, No. 22 Fasc. 2, Groupe d'étude d'Analyse ultramétrique (Y. Amice, G. Christol, P. Robba, eds.) 12 Année, 1984/1985, Paris. MR 848999 (87i:11077)

[9]

-, On the relation between Cantor's capacity and Chinburg's sectional capacity, preprint (1990).

[10]

B. A. Taylor, book review of Capacities in complex analysis, by U. Cegrell, Bull. Amer. Math. Soc. (N.S.) 24 (1991), 213-216. MR 1567903

[11]

P. Vojta, Siegel's theorem in the compact case, Annals of Math. 133 (1991), 509-548. MR 1109352 (93d:11065)

[12]

S. Zhang, Positive line bundles on arithmetic surfaces, Columbia Univ. Thesis, 1991. MR 1189866 (93j:14024)