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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Heights of projective varieties and positive Green forms
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by J.-B. Bost, H. Gillet and C. Soulé PDF
J. Amer. Math. Soc. 7 (1994), 903-1027 Request permission

Abstract:

Using arithmetic intersection theory, a theory of heights for projective varieties over rings of algebraic integers is developed. These heights are generalizations of those considered by Weil, Schmidt, Nesterenko, Philippon, and Faltings. Several of their properties are proved, including lower bounds and an arithmetic Bézout theorem for the height of the intersection of two projective varieties. New estimates for the size of (generalized) resultants are derived. Among the analytic tools used in the paper are “Green forms” for analytic subvarieties, and the existence of positive Green forms is discussed.
References
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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 7 (1994), 903-1027
  • MSC: Primary 14G40; Secondary 11G35, 14C17
  • DOI: https://doi.org/10.1090/S0894-0347-1994-1260106-X
  • MathSciNet review: 1260106