By M. Rapoport, N. Schappacher, P. Schneider
Beilinsons Conjectures on targeted Values of L-Functions bargains with Alexander Beilinsons conjectures on distinct values of L-functions. subject matters coated diversity 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 off with an advent to the Beilinson conjectures and the idea of Chern sessions from greater k-theory. The "simplest" instance of an L-function is gifted, the Riemann zeta functionality. The dialogue then turns to Delignes conjecture on severe 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 booklet concludes via reviewing the definition and homes of Deligne homology, in addition to Hodge-D-conjecture.
This monograph might be of substantial curiosity to researchers and graduate scholars who are looking to achieve a greater knowing of Beilinsons conjectures on targeted values of L-functions.
Read Online or Download Beilinson's Conjectures on Special Values of L-Functions PDF
Best number theory books
This booklet will describe the new facts of Fermat's final Theorem through Andrew Wiles, aided through Richard Taylor, for graduate scholars and college with a pretty huge heritage in algebra. it really is not easy to provide designated necessities yet a primary path in graduate algebra, masking uncomplicated teams, earrings, and fields including a passing acquaintance with quantity jewelry and types may still suffice.
Fresh Advances in Harmonic research and functions is devoted to the sixty fifth birthday of Konstantin Oskolkov and contours contributions from analysts around the globe. the amount includes expository articles by means of top specialists of their fields, in addition to chosen prime quality learn papers that discover new effects and tendencies in classical and computational harmonic research, approximation idea, combinatorics, convex research, differential equations, useful research, Fourier research, graph conception, orthogonal polynomials, distinct capabilities, and trigonometric sequence.
Creation to Cyclotomic Fields is a delicately written exposition of a critical region of quantity idea that may be used as a moment path in algebraic quantity thought. beginning at an straightforward point, the quantity covers p-adic L-functions, classification numbers, cyclotomic devices, Fermat's final Theorem, and Iwasawa's thought of Z_p-extensions, major the reader to an knowing of contemporary examine literature.
Throughout the years 1903-1914, Ramanujan labored in nearly entire isolation in India. in this time, he recorded such a lot of his mathematical discoveries with out proofs in notebooks. even though lots of his effects have been already present in the literature, so much weren't. virtually a decade after Ramanujan's loss of life in 1920, G.
- Lattice points
- A Course in Arithmetic 1996
- Elliptic Curves, Modular Forms, and Their L-functions (Student Mathematical Library, Volume 58)
- Notes on several complex variables
- Combinatorial Geometries
Additional info for Beilinson's Conjectures on Special Values of L-Functions
FiP"1 — > 0 (where TL (p) is in degree zero) and the Deligne cohomology as U V an(X'Z(P)) :=mq(X 'Z(p)P,an) ' For simplicity, in this paragraph, we drop the sub-script "an" and write Z(p)p and H 2 . 2. y x U y = jxAdy [0 if deg x = 0 if deg x > 0 otherwise . and deg y = p' U is a morphism of complexes. In fact, if we denote the differential in Z(p)p by d (where, of course, d : Z(p) — > 0 is the inclusion) and \i = deg x and ^i1 = deg y, we have: d(x U y) = x-dy \L = 0, ji' < p' x • dy -■ dxAdy |i = 0 , \L ' = p ■ \ = dx liy + (-D^xJdy dxAdy ji > 0 , |i' = p ' 0 otherwise It is quite easy to show that U is associative.
In §6 we recall the definition and some properties of the cycle class in the De Rham cohomology (following ,  and ). Especially we explain the behaviour of those classes with respect to the Hodge filtration. These constructions are needed in §7. There we first ex plain the relations between the Deligne cohomology of a projective manifold and the intermediate Jacobian of Griffiths. We reproduce Deligne's definition of the cycle class in the D - B - cohomology () and we compare it to the Abel-Jacobi map.
We have res d log = ord , kernel (J [ord ) = 0* xes and x denote the order of a zero denote the Cauchy-Poincare kernel (J |_r e s ) = fiv . 9)