# Beilinson's Conjectures on Special Values of L-Functions by M. Rapoport, N. Schappacher, P. Schneider

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

Beilinsons Conjectures on detailed Values of L-Functions offers with Alexander Beilinsons conjectures on certain values of L-functions. subject matters lined diversity from Pierre Delignes conjecture on severe values of L-functions to the Deligne-Beilinson cohomology, in addition to 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 larger 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 specialise in 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 booklet 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 certain values of L-functions.

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Gersten: Algebraic ifT-theory as generalized sheaf cohomology. In Algebraic if-Theory I, pp. 266-292, Lecture Notes in Math. 341. Deligne: Valeurs de fonctions L et p^riodes d'int^grales. Symp. , vol. 33 part 2, pp. 313-346. Soc. Dold: Lectures on Algebraic Topology. Friedlander: Etale homotopy of simplicial schemes. Studies, vol. 104. Princeton Univ. Gillet: Riemann-Roch Theorems for Higher Algebraic if-Theory. Ad vances in Math. Gillet: Comparison of K-Theory Spectral Sequences, with Applications.

R (X '^X P) The reason why this construction is not necessary in the case of a curve is just that the target group of the regulator map is m 2 (X,F* (2)) §2 and that 2 >dim^Y . 13) The Deligne-Beilinson complex In this section we want to generalize the definition cohomology in several respects. In particular we want to A. Beilinson's "theory with logarithmic growth along the - using GAGA - can be viewed as an algebraic version of cohomology (see [3]). of the Deligne explain boundary" which the Deligne For the applications to higher regulators described in this volume, A.

304-333, Lecture Notes in Math. 966. Suslin: Homology of GLn, characteristic classes and Milnor if-theory. In Algebraic if-Theory, Number Theory, Geometry and Analysis, Proc. Bielefeld 1982, pp. 357-375, Lecture Notes in Math. 1046. Tate: Algebraic cycles and poles of zeta functions. In Arithmetical Alge braic Geometry, pp. 93-111. Tate: On the conjectures of Birch and Swinnerton-Dyer and a geometric analog. In Dix exposes sur la cohomologie des schemas, pp. 189-214. Illusie: Theorie des Intersections et Theoreme de Riemann-Roch.