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An analogue of Stickelberger’s theorem for the higher K-groups. (English) Zbl 0282.12006

##### MSC:
 11R18 Cyclotomic extensions 18F25 Algebraic $$K$$-theory and $$L$$-theory (category-theoretic aspects)
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##### References:
 [1] Borel, A.: Cohomologie réelle stable des groupesS-arithmétiques classiques, C. R. Acad. Sci. Paris,274, 1700-1702 (1972) · Zbl 0235.57015 [2] Borevich, Z., Shafarevich, I.: Number Theory (translated from Russian), New York: Academic Press 1966 · Zbl 0145.04902 [3] Coates, J.: OnK 2 and some classical conjectures in algebraic number theory. Ann. of Math.95, 99-116 (1972) · Zbl 0245.12005 [4] coates, J.:K-theory and Iwasawa’s analogue of the Jacobian In: AlgebraicK-theory II, p. 502-520. Lecture Notes in Mathematics342. Berlin-Heidelberg-New York: Springer 1973 [5] Coates, J., Lichtenbaum, S.: Onl-adic zeta functions. Ann. of Math98, 498-550 (1973) · Zbl 0279.12005 [6] Coates, J., Sinnott, W.: Onp-adicL-functions over real quadratic fields (to appear) · Zbl 0305.12008 [7] Garland, H.: A finiteness theorem for theK 2 of a number field. Ann. of Math.94, 534-548 (1971) · Zbl 0247.12103 [8] Iwasawa, K.: Onp-adicL-functions. Ann. of Math.89, 198-205 (1969) · Zbl 0186.09201 [9] Leopoldt, H.: Zur Arithmetik in abelschen Zahlkörpern. J. reine angew. Math.209, 54-71 (1962) · Zbl 0204.07101 [10] Lichtenbaum, S.: Values of zeta functions, étale cohomology, and algebraicK-theory. In: AlgebraicK-theory II, p. 489-501. Lecture Notes in Mathematics342 Berlin-Heidelberg-New York: Springer 1973 [11] Milnor, J.: Introduction to algebraicK-theory. Ann. of Math. Studies,72 (1971) · Zbl 0237.18005 [12] Quillen, D.: Finite generation of the groupsK i of rings of algebraic integers. In: AlgebraicK-theory I, p. 179-198, Lecture Notes in Mathematics341, Berlin-Heidelberg-New York: Springer 1973 [13] Quillen, D.: Higher algebraicK-theory I. In: AlgebraicK-theory I, p. 85-147. Lecture Notes in Mathematics341. Berlin-Heidelberg-New York: Springer 1973 [14] Rideout, D.: A generalization of Stickelberger’s theorem. Ph. D. thesis, McGill University, Montreal 1970 [15] Siegel, C.: Über die Fourierschen Koeffizienten von Modulformen. Göttingen Nach.3, 15-56 (1970) · Zbl 0225.10031 [16] Tate, J.: Letter from Tate to Iwasawa on a relation betweenK 2 and Galois cohomology. In: AlgebraicK-theory II, p. 524-527. Lecture Notes in Mathematics342 Berlin-Heidelberg-New York: Springer 1973
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