The Noether-Lefschetz theorem and sums of 4 squares in the rational function field R(x,y)
Compositio Mathematica, Tome 86 (1993) no. 2, pp. 235-243. 
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     author = {Colliot-Th\'el\`ene, J.-L.},
     title = {The {Noether-Lefschetz} theorem and sums of 4 squares in the rational function field $R(x, y)$},
     journal = {Compositio Mathematica},
     pages = {235--243},
     publisher = {Kluwer Academic Publishers},
     volume = {86},
     number = {2},
     year = {1993},
     mrnumber = {1214459},
     zbl = {0774.12002},
     language = {en},
     url = {http://www.numdam.org/item/CM_1993__86_2_235_0/}
}
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Colliot-Thélène, J.-L. The Noether-Lefschetz theorem and sums of 4 squares in the rational function field $R(x, y)$. Compositio Mathematica, Tome 86 (1993) no. 2, pp. 235-243. http://www.numdam.org/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 | Zbl

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

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 | Zbl

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 | Zbl

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

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

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

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

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

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

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

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

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

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

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

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

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

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 | Zbl

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