By Jean Pierre Serre

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

**Best group theory books**

**A course on geometric group theory**

This quantity is meant as a self-contained advent to the elemental notions of geometric workforce concept, the most principles being illustrated with a number of examples and workouts. One target is to set up the rules of the idea of hyperbolic teams. there's a short dialogue of classical hyperbolic geometry, with the intention to motivating and illustrating this.

**Wavelets Through a Looking Glass: The World of the Spectrum**

"Mere phrases can't thoroughly describe the entire nice good points of the ebook. .. which has whatever for everybody of all mathematical persuasions. .. . This publication has really a distinct point of view from the opposite monographs on wavelets. .. regularly since it emphasizes the Fourier area because the right "window" or "looking glass" from which you can actually most simply learn wavelet concept.

**Characters of Connected Lie Groups**

This publication provides to the good physique of analysis that extends again to A. Weil and E. P. Wigner at the unitary representations of in the neighborhood compact teams and their characters, i. e. the interaction among classical team thought and smooth research. The teams studied listed below are the hooked up Lie teams of common variety (not unavoidably nilpotent or semisimple).

**G-algebras and modular representation theory**

This ebook develops a brand new method of the modular illustration thought of finite teams, introducing the reader to an lively sector of analysis in natural arithmetic. It offers a finished therapy of the idea of G-algebras and indicates the way it can be utilized to unravel a few difficulties approximately blocks, modules and almost-split sequences.

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

**Example text**

F o r the proof s e e B ourbaki, Alg . , ch. 8, §1 2 , no I, prop. 3. DEFINITION - For each prim e 1 let P1 be a rational l - adic rep re s entation of K. The sy s te m ( Pl ) i s said t o be c ompatible if P l , Pl ' are compatible for any two prime s 1 , 1 ' . The sys tem ( p ) i s said 1 to be strictly c ompatible if the r e exists a finite subset S of L K such that: = {vi Pv = d. Th e n , for every viaS u Sl' Pl is (T) ha s rational coeffic ients . unramifie d at v and P v, Pl (b) P ( T ) = Pv l (T ) g v , S u Sl u 51' .

O th e induc ed homomorphi sm o f H(O ) into l (01) = Aut(V )· If p is an 1-adic representation of Gal(K/K) 1 o into H(Q ) ' one g et s by c ompo sition a linea r 1 - adic r ep r e s entation L q, c p : Gal(K /K) � Aut( V 1 ) . U sing the fa ct that the coeffi cient s of s I. th e c h a r acte r isti c p olynomial are c e nt ral func tion s , one s e e s that GL V AB E LIAN L -ADIC REPRESENT A TIONS 1-16 4>L is rational if p rational (K a number field). Of course, compatible representations in H give compatible linear representa tions.

Let p, p ' be rational i, i' -adic r ep re s entation s of K which are c OITlpatible and s eITli - s iITlpl e . ( i ) If p is abelian ( i . e . , if IITl( p ) i s abelian) , i s it true th_a t p ' is abelian? ( W e shall s ee in c hapte r III that thi s is true at lea st if p is "loc ally algebraic " . ) .... ] ( ii ) I s it true that IITl( p ) and IITl( p ' ) are Lie g r oup s of the 1-13 J. - ADIC REPRESENT ATIONS More optimistically, is it true that there exists a same dimension? Li e alg eb r a Li e (I m (p l » 5.