The Noether-Lefschetz theorem and sums of 4 squares in the rational function field R(x,y)
Colliot-Thélène, J.-L.
Compositio Mathematica, Tome 89 (1993), p. 235-243 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1993-01-01
@article{CM_1993__86_2_235_0,
     author = {Colliot-Th\'el\`ene, Jean-Louis},
     title = {The Noether-Lefschetz theorem and sums of 4 squares in the rational function field $R(x, y)$},
     journal = {Compositio Mathematica},
     volume = {89},
     year = {1993},
     pages = {235-243},
     mrnumber = {1214459},
     zbl = {0774.12002},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CM_1993__86_2_235_0}
}

Colliot-Thélène, J.-L. The Noether-Lefschetz theorem and sums of 4 squares in the rational function field $R(x, y)$. Compositio Mathematica, Tome 89 (1993) pp. 235-243. http://gdmltest.u-ga.fr/item/CM_1993__86_2_235_0/

1 A. Buium: Sur le nombre de Picard des revêtements doubles des surfaces algébriques, C.R. Acad. Sc. Paris 296 (1983) Série I, 361-364. | MR 699163 | Zbl 0543.14017

2 J.W.S. Cassels: On the representation of rational functions as sums of squares, Acta Arithmetica 9 (1964), 79-82. | MR 162791 | Zbl 0131.25001

3 J W. S. Cassels, W. Ellison and A. Pfister: On sums of squares and on elliptic curves over function fields, J. Number Theory 3 (1971), 125-149. | MR 292781 | Zbl 0217.04302

4 M.R. Christie: Positive definite rational functions in two variables which are not the sum of three squares, J. Number Theory 8 (1976), 224-232. | MR 412162 | Zbl 0331.14017

5 J.-L. Colliot-Thélène:Real rational surfaces without a real point, Archiv der Mathematik. 58 (1992) 392-396. | MR 1152629 | Zbl 0738.14023

6 P. Deligne: Le théorème de Noether, in SGA 7 II, exp. XIX, Springer L.N.M. 340 (1973), 328-340. | Zbl 0269.14019

7 C. Delorme: Espaces projectifs anisotropes, Bull. Soc. Math. France 103 (1975), 203-223. | Numdam | MR 404277 | Zbl 0314.14016

8 I. Dolgachev: Weighted projective varieties, in Springer L.N.M. 956 (1982), 34-71. | MR 704986 | Zbl 0516.14014

9 L. Ein: An analogue of Max Noether's theorem, Duke Mathematical Journal 52 (1985), 689-706. | MR 808098 | Zbl 0589.14034

10 T. Ford: The Brauer group and ramified double covers of surfaces, preprint 1991. | MR 1191982 | Zbl 0779.13002

11 P. Griffiths and J. Harris: On the Noether-Lefschetz theorem and some remarks on codimension-two cycles, Math. Ann. 271 (1985), 31-51. | MR 779603 | Zbl 0552.14011

12 D. Hilbert: Ueber die Darstellung definiter Formen als Summe von Formenquadraten, Math. Ann. 42 (1888), 342-350. | JFM 20.0198.02 | MR 1510517

13 D. Hilbert: Ueber ternäre definite Formen, Acta Math. 17 (1893), 169-197. | JFM 25.0319.01 | MR 1554835

14 T.-Y. Lam: The algebraic theory of quadratic forms, Benjamin/Cummings 1973. | MR 634798 | Zbl 0437.10006

15 E. Landau: Ueber die Darstellung definiter Funktionen durch Quadrate, Math. Ann. 62 (1906), 272-285. | JFM 37.0252.01 | MR 1511376

16 S. Lefschetz: On certain numerical invariants of algebraic varieties with application to Abelian varieties, Trans. Amer. Math. Soc. 22 (1921), 327-482. | JFM 48.0428.03 | MR 1501178

17 S. Mori: On a generalisation of complete intersections, J. of Math. of Kyoto University 15 (1975), 619-646. | MR 393054 | Zbl 0332.14019

18 J. Steenbrink: On the Picard group of certain smooth surfaces in weighted projective space, in Algebraic geometry, Proceedings, La Rabida, 1981, Springer L.N.M. 961 (1982), 302-313. | MR 708341 | Zbl 0507.14025

19 T. Terasoma: Complete intersections with middle Picard number 1 defined over Q, Math. Z. 189 (1985), 289-296. | MR 779223 | Zbl 0579.14006