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.
Read or Download Beilinson's Conjectures on Special Values of L-Functions PDF
Similar number theory books
A textual content according to classes taught effectively over a long time at Michigan, Imperial collage and Pennsylvania kingdom.
This quantity positive aspects the result of the authors' investigations at the improvement and alertness of numerical-analytic tools for usual nonlinear boundary price difficulties (BVPs). The equipment into account provide a chance to resolve the 2 very important difficulties of the BVP thought, specifically, to set up lifestyles theorems and to construct approximation suggestions
Within the final fifteen years the Iwasawa concept has been utilized with awesome luck to elliptic curves with advanced multiplication. a transparent but basic exposition of this idea is gifted during this book.
Following a bankruptcy on formal teams and native devices, the p-adic L features of Manin-Vishik and Katz are built and studied. within the 3rd bankruptcy their relation to category box conception is mentioned, and the functions to the conjecture of Birch and Swinnerton-Dyer are handled in bankruptcy four. complete proofs of 2 theorems of Coates-Wiles and of Greenberg also are offered during this bankruptcy that may, additionally, be used as an creation to the newer paintings of Rubin.
The booklet is essentially self-contained and assumes familiarity basically with basic fabric from algebraic quantity conception and the speculation of elliptic curves. a few effects are new and others are provided with new proofs.
- Randomness and complexity: From Leibniz to Chaitin
- Elementary Number Theory: A Problem Oriented Approach
- Elements of Algebra: Geometry, Numbers, Equations
- Drinfeld Modular Curves
Extra resources for Beilinson's Conjectures on Special Values of L-Functions
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 ). 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.