Asymptotic estimates for rational points of bounded height on flag varieties

Jeffrey Lin Thunder

Compositio Mathematica (1993)

  • Volume: 88, Issue: 2, page 155-186
  • ISSN: 0010-437X

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Thunder, Jeffrey Lin. "Asymptotic estimates for rational points of bounded height on flag varieties." Compositio Mathematica 88.2 (1993): 155-186. <http://eudml.org/doc/90243>.

@article{Thunder1993,
author = {Thunder, Jeffrey Lin},
journal = {Compositio Mathematica},
keywords = {rational points; projective variety; flag variety; height; asymptotic formula},
language = {eng},
number = {2},
pages = {155-186},
publisher = {Kluwer Academic Publishers},
title = {Asymptotic estimates for rational points of bounded height on flag varieties},
url = {http://eudml.org/doc/90243},
volume = {88},
year = {1993},
}

TY - JOUR
AU - Thunder, Jeffrey Lin
TI - Asymptotic estimates for rational points of bounded height on flag varieties
JO - Compositio Mathematica
PY - 1993
PB - Kluwer Academic Publishers
VL - 88
IS - 2
SP - 155
EP - 186
LA - eng
KW - rational points; projective variety; flag variety; height; asymptotic formula
UR - http://eudml.org/doc/90243
ER -

References

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  1. [BV] E. Bombieri and J. Vaaler, On Siegel's lemma, Inv. Math.73 (1983), 11-32. Zbl0533.10030MR707346
  2. [C] J. Cassels, An Introduction to the Geometry of Numbers, Springer Grundlehren 99, Berlin, 1959. Zbl0086.26203
  3. [CS] G. Cornell and J. Silverman (eds.), Arithmetric Geometry, Springer-Verlag, New York, 1986. Zbl0596.00007
  4. [HP] W. Hodge and D. Pedoe, Methods of Algebraic Geometry, Cambridge Univ. Press, Cambridge, 1947. Zbl0796.14001MR28055
  5. [FMT] J. Franke, Y. Manin, and Y. Tschinkel, Rational points of bounded height on Fano varieties, Inv. Math.95 (1989), 421-435. Zbl0674.14012MR974910
  6. [L] S. Lang, Algebraic Number Theory, Springer-Verlag GTM 110, Berlin, 1986. Zbl0601.12001MR1282723
  7. [S] S. Schanuel, Heights in number fields, Bull. Soc. Math. France107 (1979), 433-449. Zbl0428.12009MR557080
  8. [Sch] W. Schmidt, On heights of algebraic subspaces and diophantine approximation, Ann. of Math.85 (1967), 430-472. Zbl0152.03602MR213301
  9. [Si] W. Sierpinski, O pewnem zagadnieniu z rachunku funkcyj asymptotycznych, Prace Mat.-Fiz., 17 (1906), 77-118. 
  10. [T1] J. Thunder, An asymptotic estimate for heights of algebraic subspaces, Trans. Amer. Math. Soc.331 (1992), 395-424. Zbl0773.11041MR1072102
  11. [T2] —, An Asymptotic Estimate for heights of Algebraic Subspaces, Ph.D. Thesis, Univ. of Colorado, Boulder, 1990. 
  12. [T3] —, The Number of Solutions of Bounded Height to a System of Linear Equations, Journal of Number Theory43, No. 2 (1993), 228-250. Zbl0773.11022

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