Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-28T08:09:42.062Z Has data issue: false hasContentIssue false
  • English
  • Français

Exponential sums and rational points on complete intersections

Published online by Cambridge University Press:  26 February 2010

Igor E. Shparlinskiĭ  and
Alexei N. Skorobogatov
Igor E. Shparlinskiĭ
Affiliation:
2V-41, Mosfilmovskaya Ul., Moscow 1192851, USSR.
Alexei N. Skorobogatov
Affiliation:
Institute for Problems of Information Transmission, Academy of Sciences of the USSR, 19 Ermolovoy ul., Moscow 101447, USSR.
Get access

Extract

Nous estimons le module des sommes trigonométriques sur la variété de dimension n – s definie par s formes en n variables, avec une forme linéaire en exposant. Cela s'applique a l'étude de la distribution des points rationnels d'une telle variété definie sur un corps fini ou sur le corps des nombres rationnels.

Type
Research Article
Information
Mathematika , Volume 37 , Issue 2 , December 1990 , pp. 201 - 208
Copyright
Copyright © University College London 1990

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Katz, N. M. and Laumon, G.. Transformation de Fourier et majoration de sommes exponentielles. Publ. Math. IHES, 62 (1985), 145–202.CrossRefGoogle Scholar
2. Deligne, P.. La conjecture de Weil. I. Publ. Math. IHES, 43 (1974), 273–307.CrossRefGoogle Scholar
3. Deligne, P.. La conjecture de Weil. II. Publ. Math. IHES, 52 (1980), 137–252.CrossRefGoogle Scholar
4. Myerson, G.. The distribution of rational points on varieties defined over a finite field. Mathematika, 28 (1981), 153–159.CrossRefGoogle Scholar
5. Baker, R. C.. Small solution of congruences. Mathematika, 30 (1983), 164–188.Google Scholar
6. Franke, J., Manin, Yu. I. and Tschinkel, Yu.. Rational points of bounded height on Fano varieties. Invent. Math., 95 (1989), 421–435.CrossRefGoogle Scholar
7. Batyrev, V. V. and Manin, Yu. I.. Sur le nombre des points rationnels de hauteur borné des variétés algébriques. Math. Annalen, 286 (1990), 27–43.Google Scholar
8. Schmidt, W. M.. The density of integer points on homogeneous varieties. Acta Math., 154 (1985), 243–296.CrossRefGoogle Scholar
9. Schmidt, W. M.. Simultaneous rational zeroes of quadratic forms. In: Seminaire Delange- Pisot-Poitou 1980–1981. Progress in Math., 22 (Birkhauser, 1982), 281–307.Google Scholar
10. Fujiwara, M.. Upper bounds for the number of lattice points on hypersurfaces. In: Number Theory and Combinatorics. Ed. by Akiyama, J. et al. (World Scientific Publishers, 1985), 89–96.Google Scholar
11. Fujiwara, M.. Distribution of rational points on varieties over finite fields. Mathematika, 35 (1988), 155–171.Google Scholar
12. Grothendieck, A. (with Deligne, P. and Katz, N. M.). Groupes de monodromie en géométrie algébrique. Lecture Notes in Math., 288, 340 (Springer, 1971).Google Scholar
13. Milne, J. S.. Étale cohomology. Princeton Math. Series, 33 (Princeton Univ. Press, 1980).Google Scholar
14. Fulton, W. and Lazarfeld, R.. Connectivity and its applications in algebraic geometry. In: Lecture Notes in Math., 862 (Springer, 1981).Google Scholar
15. Deligne, P. (with Boutot, J.-F., Illusie, L. and Verdier, J.-L.). Cohomologie étale. Lecture Notes in Math., 569 (Springer, 1977).Google Scholar