Gruppo Tesmed Books

Group Theory

Download e-book for kindle: Abelian L-Adic Representations and Elliptic Curves (Advanced by Jean Pierre Serre

By Jean Pierre Serre

ISBN-10: 0201093847

ISBN-13: 9780201093841

Show description

Read Online or Download Abelian L-Adic Representations and Elliptic Curves (Advanced Book Classics) PDF

Best group theory books

New PDF release: Commutative Algebra II

Covers themes akin to valuation conception; thought of polynomial and gear sequence earrings; and native algebra. This quantity contains the algebro-geometric connections and purposes of the simply algebraic fabric.

George M. Bergman's Cogroups and Co-rings in Categories of Associative Rings PDF

This publication stories representable functors between famous sorts of algebras. All such functors from associative jewelry over a set ring $R$ to every of the types of abelian teams, associative jewelry, Lie earrings, and to numerous others are made up our minds. effects also are bought on representable functors on types of teams, semigroups, commutative earrings, and Lie algebras.

Additional info for Abelian L-Adic Representations and Elliptic Curves (Advanced Book Classics)

Example text

N= l n= l The re is cons ide rable nume rical evidence fo r thi s , ba s e d on the c on ­ g ruenc e p r op e r tie s of T (Swinne rton - Dye r , unpublished) ; of c our s e , such a P would b e o f dime ns ion 2, and i t s exc eptional s e t J be empty . � [ p r o v e d b y D elign e : s e e [ 4 9 ] . [ 5 0 ] . [ 6 5 ] • S woul d . . M o r e g e ne rally, the r e s e e m s to b e a cl o s e c onne c tion between AB ELIAN 1 -18 mo dula r fo r m s , . s u c h as L: 7 ( n} x n , £ - A DI C R E P R E S E N T A TIONS and r a t i onal ( o r a l g eb r a ic ) £ - a dic r e p r e s e nta t i on s ; s e e fo r in s ta nc e Shimu r a [ 3 3 ] and W e il [4 5 ] .

N=l In all known cases, there exists a constant k such that I >--. v I -< (Nv) k, and this implies that L is convergent in some half plane R(s) > C ; P one conjectures it extends to a meromorphic function in the whole This is a formal Dirichlet series 1, 1 -1 7 l -ADIC REPRESENTATIONS pla n e . When P C OITl e s f r o m l -a d i c c ohoITl o l og y , the r e a r e s o me fu r the r c o nj e c tu r e s o n th e z e r o s and p o l e s o f the s e , a s indic a t e d by Tat e , ITlay be appl i e d p r o p e r ti e s of th e F r ob e n iu s e l e ITl ent s , d.

II o. c ons tant l ' alge - Remarks 1) Let k' be an extens ion of k and A' = A X k' We may k apply the ab ove c on s tr uction to the k ' - algebraic g r oup A' , with r e s pe ct to the exact s e quence (* ) and to the map Y 1 � A (k ) � A ' (k ' ) . The g r oup B I thus obtaine d is c anonically is omorphic to B X k ' k this follows , for ins tanc e , fr om the explic it c ons truction of B and B' . 2 ) We will only us e the ab ove c on s tr uction when char (k) and A is a torus . The enlarge d g r oup B = 0 is then a " g roup of multi ­ plicative type " ; thi s means that , afte r a s uitable finite extens ion of the gr ound field, B b e c ome s is omorphic to the pr oduct of a torus and a finite abelian group .

Download PDF sample

Abelian L-Adic Representations and Elliptic Curves (Advanced Book Classics) by Jean Pierre Serre


by David
4.3

Rated 4.76 of 5 – based on 46 votes