## On Fermat varieties.(English)Zbl 0415.14022

### MSC:

 14J25 Special surfaces 14G99 Arithmetic problems in algebraic geometry; Diophantine geometry 11D41 Higher degree equations; Fermat’s equation 14M20 Rational and unirational varieties 14C99 Cycles and subschemes

### Keywords:

algebraic cycles; unirational variety; Fermat variety
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### References:

 [1] Z. I. BOREVICH AND I. R. SAFAREViCH, Number Theory, Academic Press, New York and London, 1966. [2] A. GROTHENDIECK, Sur quelques points d’algebre homologique, Thoku Math. J., 9 (1957), 119-221. · Zbl 0118.26104 [3] A. GROTHENDIECK, Cohomologie £-adique et Fonctions L (SGA 5), Lecture Notes in Math., 589 (1977), Springer, Berlin-Heidelberg-New York. · Zbl 0345.00010 [4] R. HOTTA AND K. MATSUI, On a lemma of Tate-Thompson, Hiroshima Math. J., 8(1978), 255-268. · Zbl 0404.14001 [5] N. SASAKURA, On some results on the Picard numbers of certain algebraic surfaces, J. Math. Soc. Japan, 20 (1968), 297-321. · Zbl 0202.51801 [6] T. SHIODA, An example of unirational surfaces in characteristic p, Math. Ann., 211 (1974), 233-236. · Zbl 0276.14018 [7] T. SHIODA, On unirationality of supersingular surfaces, Math. Ann., 225 (1977), 155-159 · Zbl 0341.14010 [8] T. SHIODA, Some results on unirationality of algebraic surfaces, Math. Ann., 230 (1977), 153-168. · Zbl 0343.14021 [9] J. TATE, Algebraic cycles and poles of zeta functions, in Arithmetical Algebrai Geometry, Harper and Row, New York, 1965, 93-110. · Zbl 0213.22804 [10] J. TATE, Endomorphisms of abelian varieties over finite fields, Inventiones Math., 2 (1966), 134-144. · Zbl 0147.20303 [11] A. WEIL, Number of solutions of equations in finite fields, Bull. Amer. Math. Soc., 5 (1949), 497-508. · Zbl 0032.39402 [12] A. WEIL, Jacobi sums as ”Grossencharaktere”, Trans. Amer. Math. Soc., 73 (1952), 487-495 JSTOR: · Zbl 0048.27001
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