Download Arithmetic theory of elliptic curves: lectures given at the by J. Coates, R. Greenberg, K.A. Ribet, K. Rubin, C. Viola PDF

By J. Coates, R. Greenberg, K.A. Ribet, K. Rubin, C. Viola

This quantity comprises the improved types of the lectures given through the authors on the C. I. M. E. tutorial convention held in Cetraro, Italy, from July 12 to 19, 1997. The papers accrued listed here are extensive surveys of the present learn within the mathematics of elliptic curves, and in addition comprise a number of new effects which can't be discovered somewhere else within the literature. due to readability and style of exposition, and to the historical past fabric explicitly integrated within the textual content or quoted within the references, the amount is definitely suited for learn scholars in addition to to senior mathematicians.

Show description

Read or Download Arithmetic theory of elliptic curves: lectures given at the 3rd session of the Centro internazionale matematico estivo PDF

Best popular & elementary books

Algebra: An Elementary Text-Book for the Higher Classes of Secondary Schools and for Colleges. Part 1

This Elibron Classics e-book is a facsimile reprint of a 1904 variation by way of Adam and Charles Black, London.

Fast solvers for mesh-based computations

Quick Solvers for Mesh-Based Computations offers an alternate means of creating multi-frontal direct solver algorithms for mesh-based computations. It additionally describes the way to layout and enforce these algorithms. The book’s constitution follows these of the matrices, ranging from tri-diagonal matrices because of one-dimensional mesh-based tools, via multi-diagonal or block-diagonal matrices, and finishing with common sparse matrices.

Disk-based algorithms for big data

Disk-Based Algorithms for giant information is a manufactured from contemporary advances within the components of massive facts, info analytics, and the underlying dossier structures and knowledge administration algorithms used to aid the garage and research of big information collections. The publication discusses tough disks and their effect on info administration, considering that hard drive Drives stay universal in huge info clusters.

Additional resources for Arithmetic theory of elliptic curves: lectures given at the 3rd session of the Centro internazionale matematico estivo

Sample text

Conjecturally, this power series should be in A. This is proven in [St] if E[p] is irreducible as a GQ-module. In general, it is only known to be A @zp$,. That is, p t f y ' ( ~ )E A for some t 2 0. Kato then proves that the characteristic ideal at least contains pm f y l (T) for some m 0. Rohrlich proves that L(E/$, $,I) # 0 for all but finitely many characters $ of r, which is equivalent to the statement f y ' ( ~ )# 0 as an element of A @zp Qp. 10 in these notes). This will be discussed in [GrVa].

Then by (2) we see that H1(F,, C) is divisible. The Zp-corank of H1(F,, C) is [F, : $,I + 6, where 6 = 0 if $ is nontrivial, 6 = 1 if $ is trivial. By the inflation-restriction sequence we see that H' ((F,),, C)rv E ( $ , / Z , ) [ ~ ~ : ~ PIt~follows . ,[[r,]]-cofree of corank [F, : $,I, under the hypotheses that $ is unrapified and e, p - 2. These remarks are a special case of results proved in [Gr2]. Now we return to the case where C, = ker(E[pw] + &PI). The action of GF, on C, is by a character $, the action on is by a character 4, and we have $$ = x since the Weil pairing T,(E) A T,(E) E Z p ( l ) means that x is the determinant of the representation of GFv on T,(E).

Omitting the details, one obtains a functional equation for Lp(E/$, s): for all s E Z,. Here WE is the sign which occurs in the functional equation for the Hasse-Weil L-series L(E/$, s), NE is the conductor of E, and (NE) is the projection of NE to 1 2pZp as above. 13 and the above functional equation for the padic L-function Lp(E/$, s). The functional equation is in fact equivalent to the relation between f g n a l ( ~and ) T) f r l ( ( l +T) -' - 1) mentioned above. In particular, f ~ ~ l ( ~ ~ ) / f ?

Download PDF sample

Rated 4.64 of 5 – based on 36 votes