Geodesic
On the intersection index of divisors
Izvestiya. Mathematics, Tome 17 (1981) no. 2, pp. 343-352 
V. G. Lomadze. On the intersection index of divisors. Izvestiya. Mathematics, Tome 17 (1981) no. 2, pp. 343-352. http://geodesic.mathdoc.fr/item/IM2_1981_17_2_a5/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Using an idea of A. N. Parshin, a formula for the intersection index of Cartier divisors on an arbitrary complete variety is introduced. This formula is analogous to one for the degree of a divisor on a complete nonsingular curve expressed with the aid of canonical discrete valuations. Bibliography: 4 titles.

[1] Parshin A. N., “Polya klassov i algebraicheskaya $K$-teoriya”, Uspekhi mat. nauk, 30:1(181) (1975), 253–254 | MR | Zbl

[2] Quillen D., “Higher algebraic $K$-theory”, Lect. Notes Math., 341, 1973, 85–147 | MR | Zbl

[3] Shafarevich I. R., Osnovy algebraicheskoi geometrii, Nauka, M., 1972 | MR | Zbl

[4] Zarisskii O., Samyuel P., Kommutativnaya algebra, t. I, II, IL, M., 1963