دانلود کتاب Beilinson's Conjectures on Special Values of L-Functions

Beilinsons Conjectures on Special Values of L-Functions deals with Alexander Beilinsons conjectures on special values of L-functions. Topics covered range from Pierre Delignes conjecture on critical values of L-functions to the Deligne-Beilinson cohomology, along with the Beilinson conjecture for algebraic number fields and Riemann-Roch theorem. Beilinsons regulators are also compared with those of Émile Borel.Comprised of 10 chapters, this volume begins with an introduction to the Beilinson conjectures and the theory of Chern classes from higher k-theory. The "simplest" example of an L-function is presented, the Riemann zeta function. The discussion then turns to Delignes conjecture on critical values of L-functions and its connection to Beilinsons version. Subsequent chapters focus on the Deligne-Beilinson cohomology; ?-rings and Adams operations in algebraic k-theory; Beilinson conjectures for elliptic curves with complex multiplication; and Beilinsons theorem on modular curves. The book concludes by reviewing the definition and properties of Deligne homology, as well as Hodge-D-conjecture.This monograph should be of considerable interest to researchers and graduate students who want to gain a better understanding of Beilinsons conjectures on special values of L-functions.