Positive line bundles on arithmetic varieties
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- by Shouwu Zhang
- J. Amer. Math. Soc. 8 (1995), 187-221
- DOI: https://doi.org/10.1090/S0894-0347-1995-1254133-7
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References
- S. Ju. Arakelov, An intersection theory for divisors on an arithmetic surface, Izv. Akad. Nauk SSSR Ser. Mat. 38 (1974), 1179–1192 (Russian). MR 0472815
- Jean-Michel Bismut and Éric Vasserot, The asymptotics of the Ray-Singer analytic torsion associated with high powers of a positive line bundle, Comm. Math. Phys. 125 (1989), no. 2, 355–367. MR 1016875
- P. Deligne, Le déterminant de la cohomologie, Current trends in arithmetical algebraic geometry (Arcata, Calif., 1985) Contemp. Math., vol. 67, Amer. Math. Soc., Providence, RI, 1987, pp. 93–177 (French). MR 902592, DOI 10.1090/conm/067/902592
- Gerd Faltings, Calculus on arithmetic surfaces, Ann. of Math. (2) 119 (1984), no. 2, 387–424. MR 740897, DOI 10.2307/2007043
- Gerd Faltings, Lectures on the arithmetic Riemann-Roch theorem, Annals of Mathematics Studies, vol. 127, Princeton University Press, Princeton, NJ, 1992. Notes taken by Shouwu Zhang. MR 1158661, DOI 10.1515/9781400882472
- Henri Gillet and Christophe Soulé, Arithmetic intersection theory, Inst. Hautes Études Sci. Publ. Math. 72 (1990), 93–174 (1991). MR 1087394
- Henri Gillet and Christophe Soulé, An arithmetic Riemann-Roch theorem, Invent. Math. 110 (1992), no. 3, 473–543. MR 1189489, DOI 10.1007/BF01231343
- Robin Hartshorne, Ample subvarieties of algebraic varieties, Lecture Notes in Mathematics, Vol. 156, Springer-Verlag, Berlin-New York, 1970. Notes written in collaboration with C. Musili. MR 0282977
- Heisuke Hironaka, Resolution of singularities of an algebraic variety over a field of characteristic zero. I, II, Ann. of Math. (2) 79 (1964), 109–203; 79 (1964), 205–326. MR 0199184, DOI 10.2307/1970547
- Serge Lang, Fundamentals of Diophantine geometry, Springer-Verlag, New York, 1983. MR 715605, DOI 10.1007/978-1-4757-1810-2
- Michel Laurent, Équations diophantiennes exponentielles, Invent. Math. 78 (1984), no. 2, 299–327 (French). MR 767195, DOI 10.1007/BF01388597 P. Sarnak, Betti numbers of congruence groups, Preprint.
- L. Szpiro, Sur les propriétés numériques du dualisant relatif d’une surface arithmétique, The Grothendieck Festschrift, Vol. III, Progr. Math., vol. 88, Birkhäuser Boston, Boston, MA, 1990, pp. 229–246 (French). MR 1106917, DOI 10.1007/978-0-8176-4576-2_{9}
- Gang Tian, On a set of polarized Kähler metrics on algebraic manifolds, J. Differential Geom. 32 (1990), no. 1, 99–130. MR 1064867
- Shouwu Zhang, Positive line bundles on arithmetic surfaces, Ann. of Math. (2) 136 (1992), no. 3, 569–587. MR 1189866, DOI 10.2307/2946601
- Shouwu Zhang, Admissible pairing on a curve, Invent. Math. 112 (1993), no. 1, 171–193. MR 1207481, DOI 10.1007/BF01232429
Bibliographic Information
- © Copyright 1995 American Mathematical Society
- Journal: J. Amer. Math. Soc. 8 (1995), 187-221
- MSC: Primary 14G40; Secondary 11G35, 14G05
- DOI: https://doi.org/10.1090/S0894-0347-1995-1254133-7
- MathSciNet review: 1254133