References
Artin, M., Grothendieck, A., Verdier, J.-L.: Séminaire de géométrie algébrique —Cohomologie étale des schémas. Inst. Hautes Études Sci. (1963–4). Lecture Notes in Mathematics305. Berlin-Heidelberg-New York: Springer 1973.
Artin, M.: Algebraic construction of Brieskorn's resolution. (To appear.)
Atiyah, M.F., Singer, I.M.: The index of elliptic operators IV. Annals of Math.93, 119–138 (1971).
Borel, A.: Arithmetic properties of linear algebraic graphs. Proc. Int. Congr. Math., 1962. Uppsala: Almqvist & Wiksells 1963.
Brieskorn, E.: Singular elements of semi-simple algebraic groups. Proc. Int. Congr. Nice, 1970. Paris: Gauthier-Villars 1971.
Deligne, P.: La conjecture de Weil pour les surfacesK 3. Inventiones mat.15, 206–226 (1972).
Enriques, F.: Le superficie algebriche. Zannichelli: Bologna 1949.
Grothendieck, A.: Techniques de descente et théorèmes d'existence en géométrie algébrique V. Séminaire Bourbaki 13 (1960–61) exposé 232 (mimeographed notes).
Grothendieck, A.: Le groupe de Brauer III. Dix exposés sur la cohomologie des schémas. North-Holland: Amsterdam 1968.
Kodaira, K.: On compact analytic surfaces. Analytic Functions. pp. 121–135. Princeton 1960.
Kodaira, K., Spencer, D.C.: On deformations of complex analytic structures III. Annals of Math.71, 43–76 (1960).
Milne, J.S.: The Tate-Safarevic group of a constant abelian variety. Inventiones math.6, 91–105 (1968).
Milne, J.S.: The Brauer group of a rational surface. (To appear.)
Néron, A.: Modeles mininaux des variétés abéliennes sur les corps locaux et globaux. Pub. Math. Inst. Hautes Études Sci.21 (1964).
Tate, J.: Algebraic cycles and poles of zeta functions. Arithmetical algebraic geometry. pp. 93–110. Harper and Row: New York 1965.
Tate, J.: On the conjecture of Birch and Swinnerton-Dyer and a geometric analog. Séminaire Bourbaki 1965–66, exposé 306 (mimeographed notes).
Tate, J.: Endomorphisms of abelian varieties over finite fields. Inventiones math.2, 134–144 (1966).
Whitehead, J.H.C.: A certain exact sequence. Annals of Math.52, 51–110 (1950).
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Artin, M., Swinnerton-Dyer, H.P.F. The Shafarevich-Tate conjecture for pencils of elliptic curves onK3 surfaces. Invent Math 20, 249–266 (1973). https://doi.org/10.1007/BF01394097
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DOI: https://doi.org/10.1007/BF01394097