Higher regulators and values of L-functions
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Abstract
In the work conjectures are formulated regarding the value of L-functions of motives and some computations are presented corroborating them.
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Literature cited
- 1.S. Yu. Arakelov, “Theory of intersections of divisors on an arithmetic surface,” Izv. Akad. Nauk SSSR, Ser. Mat.,38, No. 6, 1179–1192 (1974).Google Scholar
- 2.M. F. Atiyah, K-Theory, W. A. Benjamin (1967).Google Scholar
- 3.A. A. Beilinson, “Higher regulators and values of the L-functions of curves,” Funkts. Anal. Prilozhen.,14, No. 2, 46–47 (1980).Google Scholar
- 4.A. Weil, Elliptic Functions According to Eisenstein and Kronecker, Springer-Verlag (1976).Google Scholar
- 5.H. Jacquet and R. P. Langlands, Automorphic Forms on GL(2), Springer-Verlag (1970).Google Scholar
- 6.Yu. I. Manin, “Correspondences, motifs, and monoidal transformations,” Mat. Sb.,77, No. 4, 475–507 (1968).Google Scholar
- 7.A. A. Suslin, “Algebraic K-theory,” Itogi Nauki i Tekh. VINITI. Algebra. Topologiya. Geometriya, Vol. 20 (1982), pp. 71–152.Google Scholar
- 8.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.Google Scholar
- 9.S. Bloch, “Higher regulators, algebraic K-theory, and zeta-functions of elliptic curves,” Irvine Univ. Preprint (1978).Google Scholar
- 10.S. Bloch, “Lectures on algebraic cycles,” Duke Univ. Math. Series, No. 4 (1980).Google Scholar
- 11.S. Bloch, “The dilogarithm and extensions of Lie algebras,” Lect. Notes Math.,B54, 1–23 (1981).Google Scholar
- 12.A. Borel, “Stable and real cohomology of arithmetic groups,” Ann. Sci. ENS,7, 235–272 (1974).Google Scholar
- 13.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).Google Scholar
- 14.A. K. Bousfield and D. M. Kan, “Homotopy limits, completions and localizations,” Lect. Notes Math.,304 (1972).Google Scholar
- 15.P. Deligne, “Theorie de Hodge. II,” Publ. Math. Inst. Hautes Etudes Scient.,40, 5–58 (1971).Google Scholar
- 16.P. Deligne, “Theorie de Hodge. III,” Publ. Math. Inst. Hautes Etudes Scient.,44, 5–77 (1974).Google Scholar
- 17.P. Deligne, “Les constantes des equations fonctionelles des fonctions L,” Lect. Notes Math.,349, 501–597 (1973).Google Scholar
- 18.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.Google Scholar
- 19.P. Deligne, “Le symbole modere,” Manuscript (1979).Google Scholar
- 20.P. Deligne and M. Rapoport, “Les schemas de modules de courbes elliptiques,” Lect. Notes Math.,349, 143–316 (1973).Google Scholar
- 21.J. Dupont, “Simplicial de Rham cohomology and characteristic classes of flat bundles,” Topology,15, No. 3, 233–245 (1976).CrossRefGoogle Scholar
- 22.H. Gillet, “Riemann-Roch theorems for higher algebraic K-theory,” Adv. Math.,40, 203–289 (1981).CrossRefGoogle Scholar
- 23.H. Gillet, “Comparison of K-theory spectral sequences with applications,” Lect. Notes Math., No. 854, 141–167 (1981).Google Scholar
- 24.B. Gross, “Higher regulators and values of Artin's L-functions,” Preprint (1979).Google Scholar
- 25.H. Jacquet, “Automorphic forms on GL(2),” Lect. Notes Math., No. 78 (1971).Google Scholar
- 26.Ch. Kratzer, “λ-structure en K-theorie algebrique,” Comment. Math. Helv.,55, No. 2, 233–254 (1980).Google Scholar
- 27.J.-L. Loday, “Symboles en K-theorie algebrique superiore,” C. R. Acad. Sci.,292, 863–867 (1981).Google Scholar
- 28.D. Quillen, “Higher algebraic K-theory. I,” Lect. Notes Math., No. 341 (1973).Google Scholar
- 29.B. Saint-Donat, “Technique de descent cohomologique,” Lect. Notes Math.,270, 83–162 (1972).Google Scholar
- 30.Ch. Soulé, “Operations en K-theorie algebrique,” Preprint (1980).Google Scholar
- 31.A. Suslin, “Homology of GLn, characteristic classes, and Milnor's K-theory,” Preprint, LOMI (1982).Google Scholar
- 32.J. Tate, “Algebraic cycles and poles of zeta functions,” Arithmetical Algebraic Geometry, New York (1965), pp. 93–100.Google Scholar
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© Plenum Publishing Corporation 1985