By M. Rapoport, N. Schappacher, P. Schneider

Beilinsons Conjectures on specified Values of L-Functions offers with Alexander Beilinsons conjectures on designated values of L-functions. themes coated variety from Pierre Delignes conjecture on severe values of L-functions to the Deligne-Beilinson cohomology, besides the Beilinson conjecture for algebraic quantity fields and Riemann-Roch theorem. Beilinsons regulators also are in comparison with these of Émile Borel.

Comprised of 10 chapters, this quantity starts with an advent to the Beilinson conjectures and the idea of Chern sessions from better k-theory. The "simplest" instance of an L-function is gifted, the Riemann zeta functionality. The dialogue then turns to Delignes conjecture on serious values of L-functions and its connection to Beilinsons model. next chapters concentrate on the Deligne-Beilinson cohomology; ?-rings and Adams operations in algebraic k-theory; Beilinson conjectures for elliptic curves with complicated multiplication; and Beilinsons theorem on modular curves. The publication concludes by way of reviewing the definition and homes of Deligne homology, in addition to Hodge-D-conjecture.

This monograph can be of substantial curiosity to researchers and graduate scholars who are looking to achieve a greater figuring out of Beilinsons conjectures on targeted values of L-functions.

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**Beilinson's Conjectures on Special Values of L-Functions**

Beilinsons Conjectures on certain Values of L-Functions bargains with Alexander Beilinsons conjectures on designated values of L-functions. themes coated variety from Pierre Delignes conjecture on serious values of L-functions to the Deligne-Beilinson cohomology, in addition to the Beilinson conjecture for algebraic quantity fields and Riemann-Roch theorem.

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In Algebraic If-Theory Evanston 1980, pp. 141-167, Lecture Notes in Math. 854. Gillet: Universal cycle classes. Compositio Math. SoulS: Intersection sur les vari6t£s d'Arakelov. Godement: Th£orie des faisceaux. Harris: Principles of Algebraic Geometry. Gros: Classes de Chern et classes de cycles en cohomologie de HodgeWitt logarithmique. Sc. Grothendieck: La th^orie des classes de Chern. Math. Grothendieck: Classes de Chern et representations lineaires des groupes discrets. In Dix exposes sur la cohomologie des sch^mas, pp.

In V. 18 Hk+l(Y,F) xU v If we interprete cohomology classes as homomorphisms in D(V) then x U y is given by the commutative diagram ivz(y. ) u diagonal { 7VZ£. ^ ^ [ t + fl Here E Z denotes the homotopy equivalence given by the theorem of Eilenberg-Zilber. F) O(l) — « Like the homotopy property this property (III) is of a local nature. Therefore it generalizes to arbitrary projective bundles. Proposition: Let E be a rank n vector bundle on a simplicial scheme Y. in V. ,F) -^ H*(P(E),F) is an isomorphism; here ir : ~P(E) —► Y.

Math. Grothendieck: Classes de Chern et representations lineaires des groupes discrets. In Dix exposes sur la cohomologie des sch^mas, pp. 215-305. Hartshorne: Residues and Duality. Lecture Notes in Math. 20. Hartshorne: On the de Rham cohomology of algebraic varieties. Publ. Math. Hiller: A-rings and algebraic lif-theory. Pure Appl. Jouanolou: Une suite exacte de Mayer-Vietoris en lf-th&)rie alg6brique. In Algebraic iT-Theory I, pp. 293-316, Lecture Notes in Math. 341. van der Kallen: Homology Stability for Linear Groups.