By M. Rapoport, N. Schappacher, P. Schneider
Beilinsons Conjectures on distinct Values of L-Functions bargains with Alexander Beilinsons conjectures on distinctive values of L-functions. themes coated variety from Pierre Delignes conjecture on serious 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 speculation 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 advanced multiplication; and Beilinsons theorem on modular curves. The publication concludes by means of reviewing the definition and houses of Deligne homology, in addition to Hodge-D-conjecture.
This monograph will be of substantial curiosity to researchers and graduate scholars who are looking to achieve a greater realizing of Beilinsons conjectures on distinct values of L-functions.
Read Online or Download Beilinson's Conjectures on Special Values of L-Functions PDF
Best number theory books
A pleasant creation to quantity thought, Fourth variation is designed to introduce readers to the general issues and technique of arithmetic throughout the unique research of 1 specific facet—number thought. beginning with not anything greater than simple highschool algebra, readers are steadily resulted in the purpose of actively acting mathematical examine whereas getting a glimpse of present mathematical frontiers.
Featuring quite a lot of mathematical versions which are at present utilized in existence sciences should be considered as a problem, and that's exactly the problem that this ebook takes up. in fact this panoramic examine doesn't declare to supply an in depth and exhaustive view of the numerous interactions among mathematical versions and existence sciences.
Mathematicians and non-mathematicians alike have lengthy been eager about geometrical difficulties, rather those who are intuitive within the experience of being effortless to kingdom, maybe via an easy diagram. each one part within the publication describes an issue or a gaggle of comparable difficulties. often the issues are in a position to generalization of version in lots of instructions.
- Compositions of Quadratic Forms (De Gruyter Expositions in Mathematics)
- Class Field Theory
- A Classical Introduction to Modern Number Theory (2nd Edition) (Graduate Texts in Mathematics, Volume 84)
- Cyclotomic Fields and Zeta Values
- Sieve Methods, Exponential Sums, and their Applications in Number Theory
Extra info for Beilinson's Conjectures on Special Values of L-Functions
42 DELIGNE-BEILINSON COHOMOLQGY Hele*ne Esnault* , Eckart Viehweg In these notes we describe the Deligne cohomology of a complex manifold as well as Beilinson's algebraic cohomology theory of a quasiprojective complex manifold and some of its properties. In fact, most of the content of our manuscript can be found (in a more compressed form) in the first paragraph of Beilinson's article , We tried to include all details needed, and we hope that our presentation is sufficiently "down to earth" to serve as an introduction to this theory.
We need to know in the following is that the action of the Adams operations i/>k, for k > 1, on it can be determined explicitly. ) and k > 1 we have r/>kx = (rMVxj)j>i) . Proof: We freely use the notations of SGA 6 exp. V. cit. cit. ) = ( 0 ) l , . . , f c ^ O , . . ) f o r a l U > l . cit. 3). ) = ( 0 , 1 , ( 4 ^ ) , - > ! ))t+1 holds true for all £ > 1 which proves the assertion. All the important properties of Chern classes now can be expressed by the following statement. ) of augmented # ° ( y .
3). ,P) :x0 = l} j>0 which obviously forms an abelian group with respect to the cup-product as addition (it is suggestive to think of elements in the second factor as being power series in one variable with constant coefficient 1). ) in a natural way can be made into an augmented # ° ( y . , Z ) — A-algebra, too. The interested reader should consult SGA 6 exp. 0 App. I §3 or exp. V §6 for the details. ) we need to know in the following is that the action of the Adams operations i/>k, for k > 1, on it can be determined explicitly.