Gauss sums and algebraic cycles

S. Turner

Compositio Mathematica (1987)

  • Volume: 63, Issue: 2, page 145-158
  • ISSN: 0010-437X

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Turner, S.. "Gauss sums and algebraic cycles." Compositio Mathematica 63.2 (1987): 145-158. <http://eudml.org/doc/89855>.

@article{Turner1987,
author = {Turner, S.},
journal = {Compositio Mathematica},
keywords = {-adic étale cohomology; Gauss sums; Hodge index theorem; Tate- Birch-Swinnerton-Dyer conjecture; crystalline cohomology},
language = {eng},
number = {2},
pages = {145-158},
publisher = {Martinus Nijhoff Publishers},
title = {Gauss sums and algebraic cycles},
url = {http://eudml.org/doc/89855},
volume = {63},
year = {1987},
}

TY - JOUR
AU - Turner, S.
TI - Gauss sums and algebraic cycles
JO - Compositio Mathematica
PY - 1987
PB - Martinus Nijhoff Publishers
VL - 63
IS - 2
SP - 145
EP - 158
LA - eng
KW - -adic étale cohomology; Gauss sums; Hodge index theorem; Tate- Birch-Swinnerton-Dyer conjecture; crystalline cohomology
UR - http://eudml.org/doc/89855
ER -

References

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  2. 2 P. Deligne (notes by J.S. Milne): Hodge cycles on abelian varieties. In: Hodge Cycles, Motives, and Shimura Varieties. Lecture Notes in Math.900. Springer-Verlag, Berlin, Heidelberg, New York (1982). Zbl0537.14006
  3. 3 W.J. Gordon: Linking the conjectures of Artin-Tate and Birch-Swinnerton-Dyer. Compositio Math.38, 2 (1979) 163-199. Zbl0425.14003MR528839
  4. 4 A. Grothendieck: Le groupe de Brauer III. In: Dix exposés sur la cohomologie des schémas. North-Holland, Amsterdam (1968). Zbl0198.25901
  5. 5 M. Gros: Classes de Chern et classes de cycles en cohomologie logarithmique, These 3° cycle. Universite de Paris-Sud, Centre d'Orsay (1983). Zbl0615.14011
  6. 6 P. Hriljac: Heights and Arakelov's intersection theory. Amer. J. Math.107, 1 (1986) 23-38. Zbl0593.14004MR778087
  7. 7 M. Knebush and W. Scharlau: Quadratische Formen und quadratische Reziprozitätsgesetze über algebraischen Zahlkörpern. Math. Z.121 (1971) 346-368. Zbl0216.04602MR351998
  8. 8 S. Lang: Fundamentals of Diophantine Geometry. Springer-Verlag, New York, Berlin, Heidelberg, Tokyo, (1983). Zbl0528.14013MR715605
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  10. 10 S. Lichtenbaum: Curves over discrete valuation rings. Amer. J. Math.90 (1968) 380-405. Zbl0194.22101MR230724
  11. 11 J.S. Milne: On a conjecture of Artin and Tate. Ann. Math. (2) 102 (1975) 517-533. Zbl0343.14005MR414558
  12. 12 J.S. Milne: Étale Cohomology. Princeton University Press, Princeton (1980). Zbl0433.14012MR559531
  13. 13 A. Néron: Modèles minimaux des variétés abéliennes sur les corps locaux et globaux. Inst. Hautes Études Sci. Publ. Math.21 (1964) 361-484. Zbl0132.41403MR179172
  14. 14 A. Néron: Quasi-fonctions et hauteurs sur les variétés abéliennes. Ann. Math.82 (1965) 249-331. Zbl0163.15205MR179173
  15. 15 H. Reiter: Über den Satz von Weil-Cartier. Monatsh. Math.86 (1978) 13-62. Zbl0396.43015MR510632
  16. 16 I.R. Shafarevich: Lectures on Minimal Models and Birational Transformations of Two Dimensional Schemes. Tata Institute of Fundamental Research, Bombay (1966). Zbl0164.51704MR217068
  17. 17 J. Tate: Fourier analysis in number fields and Hecke's zeta-functions. In: Algebraic Number Theory, eds. J.W.S. Cassels and A. Fröhlich. Thompson Book Company Inc., Washington, DC (1967). MR217026
  18. 18 J. Tate: Algebraic cycles and poles of zeta functions. In: Arithmetical Algebraic Geometry, ed. O.F.G. Schilling. Harper and Row, New York (1965). Zbl0213.22804MR225778
  19. 19 J. Tate: On the conjectures of Birch and Swinnerton-Dyer and a geometric analog. In: Dix exposés sur la cohomologie des schémas. North-Holland, Amsterdam (1968). Zbl0199.55604
  20. 20 A. Weil: Sur certains groupes d'opérateurs unitaires. Acta Math.111 (1964) 143-211. Zbl0203.03305MR165033
  21. 21 A. Weil: Basic Number Theory, third edition. Springer-Verlag, New York, Heidelberg, Berlin (1974). Zbl0326.12001MR427267

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