Geodesic
The Euler characteristic of a family of algebraic varieties
Sbornik. Mathematics, Tome 18 (1972) no. 2, pp. 303-319 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper we derive a formula for the $l$-adic Euler characteristic of a one-parameter family of algebraic varieties. We define an algebraic analog of the local monodromy of isolated singularities of algebraic hypersurfaces, defined in the complex case by Milnor. We discuss various conjectures connected with the definition of the conductor of a family of algebraic varieties. Bibliography: 26 titles. 
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     title = {The {Euler} characteristic of a~family of algebraic varieties},
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I. V. Dolgachev. The Euler characteristic of a family of algebraic varieties. Sbornik. Mathematics, Tome 18 (1972) no. 2, pp. 303-319. http://geodesic.mathdoc.fr/item/SM_1972_18_2_a9/

[1] I. R. Shafarevich (red.), Algebraicheskie poverkhnosti, Trudy Matem. in-ta im. V. A. Steklova, 75, 1965 | MR | Zbl

[2] Sh. Abhyankar, “On the problem of resolution of singularities”, Proc. Internat. Congr. Math. (Moscow, 1966), Mir, Moskva, 1968, 467–479 | MR

[3] I. Dolgacev, “On the purity of the degeneration loci of families of curves”, Invent. Math., 8 (1969), 34–54 | DOI | MR

[4] I. V. Dolgachev, A. N. Parshin, “Differenta i diskriminant regulyarnykh otobrazhenii”, Matem. zametki, 4:5 (1968), 519–523

[5] A. Grothendieck, Elements de Geometrie Algebrique, Publ. Math. IHES, no. 17, 24, 28, 32, Paris, 1962–1966

[6] H. Hironaka, “Resolution of singularities of an algebraic variety”, Ann. Math., 79:1 (1964), 109–326 | DOI | MR | Zbl

[7] B. Iversen, “On critical values of an algebraic function”, Invent. Math., 12 (1971), 210–224 | DOI | MR | Zbl

[8] H. Jung, Algebraische Flachen, Hannover, 1925 | Zbl

[9] Yu. I. Manin, “Lektsii o $K$-funktore v algebraicheskoi geometrii”, Uspekhi matem. nauk, XXIV:5(149) (1969), 3–86 | MR

[10] D. Mumford, Introduction into algebraic geometry, Preprint, Harvard Univ., 1969 | MR

[11] Y. Nakai, “Note on the intersection of an algebraic variety with the generic hyperplane”, Mem. Coll. Sci. Univ. Kyoto, 26:2 (1950), 185–187 | MR

[12] A. Ogg, “Cohomology of abelian varieties over function fields”, Ann. Math., 76:2 (1962), 185–212 | DOI | MR | Zbl

[13] A. Ogg, “Elliptic curves and wild ramification”, Amer. J. Math., 89:1 (1967), 1–21 | DOI | MR | Zbl

[14] M. Raynaud, “Models de Neron”, C. R. Acad Sci., 262 (1966), 413–416, Paris

[15] M. Raynaud, “Caracteristique d'Euler–Poincare d'un faisceau et cohomologie des varietés abéliennes”, Dix exsposés sur la cohomologie des schémas, North-Holland, Amsterdam, 1968, 12–31

[16] Seminaire de Geometrie Algebrique, Mimeo. Notes (SGA 4), 4, IHES, Paris, 1964–65

[17] Seminaire de Geometrie Algebrique, Mimeo. Notes (SGA 5), 5, IHES, Paris, 1964–65

[18] Seminaire de Geometrie Algebrique (SGA 7), 7, IHES, Paris, 1968–1970

[19] Zh.-P. Serr, Algebraicheskie gruppy i polya klassov, Mir, Moskva, 1967

[20] J.-P. Serre, Corps locaux, Harmann, Paris, 1962 | MR

[21] J.-P. Serre, J. Tate, “Good reduction of abelian varieties”, Ann. Math., 88:2, 1968 | MR | Zbl

[22] J.-L. Verdier, “A duality theorem in the etale cohomology”, Local fields, Diebergen, 1966, 184–198 | MR

[23] I. R. Shafarevich, “Glavnye odnorodnye prostranstva nad funktsionalnymi polyami”, Trudy Matem. in-ta im. V. A. Steklova, 64 (1961), 316–346

[24] F. Griffits, “Doklad o variatsii struktury Khodzha”, Uspekhi matem. nauk, XXV:3(153) (1970), 175–234 | MR

[25] Dzh. Milnor, Osobye tochki kompleksnykh giperpoverkhnostei, Mir, Moskva, 1971 | MR

[26] E. Brieskorn, “Die Monodromie die isolierten Singularitaten von Hyperflachen”, Manuscr. Math., 2 (1970), 103–161 | DOI | MR | Zbl