Canonical heights on varieties with morphisms

Gregory S. Call; Joseph H. Silverman

Compositio Mathematica (1993)

  • Volume: 89, Issue: 2, page 163-205
  • ISSN: 0010-437X

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Call, Gregory S., and Silverman, Joseph H.. "Canonical heights on varieties with morphisms." Compositio Mathematica 89.2 (1993): 163-205. <http://eudml.org/doc/90256>.

@article{Call1993,
author = {Call, Gregory S., Silverman, Joseph H.},
journal = {Compositio Mathematica},
keywords = {height function; non-archimedean local height pairings; intersection theory},
language = {eng},
number = {2},
pages = {163-205},
publisher = {Kluwer Academic Publishers},
title = {Canonical heights on varieties with morphisms},
url = {http://eudml.org/doc/90256},
volume = {89},
year = {1993},
}

TY - JOUR
AU - Call, Gregory S.
AU - Silverman, Joseph H.
TI - Canonical heights on varieties with morphisms
JO - Compositio Mathematica
PY - 1993
PB - Kluwer Academic Publishers
VL - 89
IS - 2
SP - 163
EP - 205
LA - eng
KW - height function; non-archimedean local height pairings; intersection theory
UR - http://eudml.org/doc/90256
ER -

References

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  2. 2. Call, G.: Variation of local heights on an algebraic family of abelian varieties. Théorie des Nombres, Berlin, (1989). Zbl0701.14022MR1024553
  3. 3. Call, G. and Silverman, J.: Computing canonical heights on K3 surfaces, in preparation. Zbl0865.14020
  4. 4. Dem'janenko, V.A.: An estimate of the remainder term in Tate's formula (Russian), Mat. Zametki3 (1968) 271-278. Zbl0161.40601MR227166
  5. 5. Dem'janenko, V.A.: Rational points of a class of algebraic curves, AMS Translations (2) 66 (1968) 246-272. Zbl0181.24001
  6. 6. Green, W.: Heights in families of abelian varieties, Duke Math. J.58 (1989) 617-632. Zbl0698.14043MR1016438
  7. 7. Hartshorne, R.: Algebraic Geometry, Springer-Verlag, New York, (1977). Zbl0367.14001MR463157
  8. 8. Lang, S.: Fundamentals of Diophantine Geometry, New York, (1983). Zbl0528.14013MR715605
  9. 9. Lang, S.: Number Theory III: Diophantine Geometry. Encycl. Math. Sci. v. 60, Springer-Verlag, Berlin, (1991). Zbl0744.14012MR1112552
  10. 10. Lewis, D.J.: Invariant sets of morphisms on projective and affine number spaces, J. Algebra20 (1972) 419-434. Zbl0245.12003MR302602
  11. 11. Manin, Ju.: The p-torsion of elliptic curves is uniformly bounded. Izv. Akad. Nauk. SSSR33 (1969) 433-438. Zbl0205.25002MR272786
  12. 12. Manin, Ju. and Zarhin, Ju.: Height on families of abelian varieties, Math. USSR Sbor.18 (1972) 169-179. Zbl0263.14011
  13. 13. Narkiewicz, W.: On polynomial transformations in several variables, Acta Arith.11 (1965) 163-168. Zbl0148.41801MR186625
  14. 14. Néron, A.: Quasi-fonctions et hauteurs sur les variétés abéliennes, Annals of Math.82 (1965) 249-331. Zbl0163.15205MR179173
  15. 15. Silverman, J.H.: Heights and the specialization map for families of abelian varieties, J. Reine Angew. Math.342 (1983) 197-211. Zbl0505.14035MR703488
  16. 16. Silverman, J.H.: The Arithmetic of Elliptic Curves, Springer, New York, (1986). Zbl0585.14026MR817210
  17. 17. Silverman, J.H.: Arithmetic distance functions and height functions in Diophantine geometry, Math. Ann.279 (1987) 193-216. Zbl0607.14013MR919501
  18. 18. Silverman, J.H.: Computing heights on elliptic curves, Math. Comp.51 (1988) 339-358. Zbl0656.14016MR942161
  19. 19. Silverman, J.H.: Rational points on K3 surfaces: A new canonical height, Invent. Math.105 (1991) 347-373. Zbl0754.14023MR1115546
  20. 20. Silverman, J.H.: Variation of the canonical height on elliptic surfaces I: Three examples, J. Reine Angew. Math.426 (1992) 151-178. Zbl0739.14023MR1155751
  21. 21. Tate, J.: Letter to J.-P. Serre, Oct. 1, (1979). 
  22. 22. Tate, J.: Variation of the canonical height of a point depending on a parameter, Amer. J. Math.105 (1983) 287-294. Zbl0618.14019MR692114
  23. 23. Wehler, J.: K3-surfaces with Picard number 2, Arch. Math.50 (1988) 73-82. Zbl0602.14038MR925498
  24. 24. Wehler, J.: Hypersurfaces of the Flag Variety, Math. Zeit.198 (1988) 21-38. Zbl0662.14029MR938026
  25. 25. Zimmer, H.: On the difference of the Weil height and the Néron-Tate height, Math. Z.174 (1976) 35-51. Zbl0303.14003MR419455

Citations in EuDML Documents

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  1. Xander Faber, Adam Towsley, Newton’s method over global height fields
  2. Atsushi Sato, On the distribution of rational points on certain Kummer surfaces
  3. Matthew H. Baker, Robert Rumely, Equidistribution of Small Points, Rational Dynamics, and Potential Theory
  4. Joseph H. Silverman, The field of definition for dynamical systems on 1
  5. Liang-Chung Hsia, A weak Néron model with applications to p -adic dynamical systems
  6. Laurent Denis, Problème de Lehmer en caractéristique finie
  7. Pascal Autissier, Équidistribution des sous-variétés de petite hauteur

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