Abstract
In the work conjectures are formulated regarding the value of L-functions of motives and some computations are presented corroborating them.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
S. Yu. Arakelov, “Theory of intersections of divisors on an arithmetic surface,” Izv. Akad. Nauk SSSR, Ser. Mat.,38, No. 6, 1179–1192 (1974).
M. F. Atiyah, K-Theory, W. A. Benjamin (1967).
A. A. Beilinson, “Higher regulators and values of the L-functions of curves,” Funkts. Anal. Prilozhen.,14, No. 2, 46–47 (1980).
A. Weil, Elliptic Functions According to Eisenstein and Kronecker, Springer-Verlag (1976).
H. Jacquet and R. P. Langlands, Automorphic Forms on GL(2), Springer-Verlag (1970).
Yu. I. Manin, “Correspondences, motifs, and monoidal transformations,” Mat. Sb.,77, No. 4, 475–507 (1968).
A. A. Suslin, “Algebraic K-theory,” Itogi Nauki i Tekh. VINITI. Algebra. Topologiya. Geometriya, Vol. 20 (1982), pp. 71–152.
S. Bloch, “Applications of the dilogarithm function in algebraic K-theory and algebraic geometry,” Proc. Int. Symp. on Alg. Geometry, Kyoto (1977), pp. 103–114.
S. Bloch, “Higher regulators, algebraic K-theory, and zeta-functions of elliptic curves,” Irvine Univ. Preprint (1978).
S. Bloch, “Lectures on algebraic cycles,” Duke Univ. Math. Series, No. 4 (1980).
S. Bloch, “The dilogarithm and extensions of Lie algebras,” Lect. Notes Math.,B54, 1–23 (1981).
A. Borel, “Stable and real cohomology of arithmetic groups,” Ann. Sci. ENS,7, 235–272 (1974).
A. Borel, “Cohomologie de SLn et valeurs de fonctions zeta aux points entiers,” Ann. Scu. Norm. Super. Pisa Cl. Sci.,4, No. 4, 613–636 (1977).
A. K. Bousfield and D. M. Kan, “Homotopy limits, completions and localizations,” Lect. Notes Math.,304 (1972).
P. Deligne, “Theorie de Hodge. II,” Publ. Math. Inst. Hautes Etudes Scient.,40, 5–58 (1971).
P. Deligne, “Theorie de Hodge. III,” Publ. Math. Inst. Hautes Etudes Scient.,44, 5–77 (1974).
P. Deligne, “Les constantes des equations fonctionelles des fonctions L,” Lect. Notes Math.,349, 501–597 (1973).
P. Deligne, “Valeurs de fonctions L et periodes d'integrales,” Automorphic Forms, Representations, and L-Functions, Proc. Symp. Pure Math. Am. Math. Soc., Corvallis, Ore. (1977), Part 2, Providence, R.I. (1979), pp. 313–346.
P. Deligne, “Le symbole modere,” Manuscript (1979).
P. Deligne and M. Rapoport, “Les schemas de modules de courbes elliptiques,” Lect. Notes Math.,349, 143–316 (1973).
J. Dupont, “Simplicial de Rham cohomology and characteristic classes of flat bundles,” Topology,15, No. 3, 233–245 (1976).
H. Gillet, “Riemann-Roch theorems for higher algebraic K-theory,” Adv. Math.,40, 203–289 (1981).
H. Gillet, “Comparison of K-theory spectral sequences with applications,” Lect. Notes Math., No. 854, 141–167 (1981).
B. Gross, “Higher regulators and values of Artin's L-functions,” Preprint (1979).
H. Jacquet, “Automorphic forms on GL(2),” Lect. Notes Math., No. 78 (1971).
Ch. Kratzer, “λ-structure en K-theorie algebrique,” Comment. Math. Helv.,55, No. 2, 233–254 (1980).
J.-L. Loday, “Symboles en K-theorie algebrique superiore,” C. R. Acad. Sci.,292, 863–867 (1981).
D. Quillen, “Higher algebraic K-theory. I,” Lect. Notes Math., No. 341 (1973).
B. Saint-Donat, “Technique de descent cohomologique,” Lect. Notes Math.,270, 83–162 (1972).
Ch. Soulé, “Operations en K-theorie algebrique,” Preprint (1980).
A. Suslin, “Homology of GLn, characteristic classes, and Milnor's K-theory,” Preprint, LOMI (1982).
J. Tate, “Algebraic cycles and poles of zeta functions,” Arithmetical Algebraic Geometry, New York (1965), pp. 93–100.
Additional information
Translated from Itogi Nauki i Tekhniki, Seriya Sovremennye Problemy Matematiki (Noveishie Dostizheniya), Vol. 24, pp. 181–238, 1984.
Rights and permissions
About this article
Cite this article
Beilinson, A.A. Higher regulators and values of L-functions. J Math Sci 30, 2036–2070 (1985). https://doi.org/10.1007/BF02105861
Issue Date:
DOI: https://doi.org/10.1007/BF02105861