Download Abelian L-Adic Representations and Elliptic Curves (Advanced by Jean Pierre Serre PDF
By Jean Pierre Serre
Read or Download Abelian L-Adic Representations and Elliptic Curves (Advanced Book Classics) PDF
Similar group theory books
Those notes provide an account of modern paintings in harmonic research facing the analytical foundations of A. Weil's concept of metaplectic teams. it truly is proven that Weil's major theorem holds for a category of services (a sure Segal algebra) better than that of the Schwartz-Bruhat capabilities thought of via Weil.
This is often the second one of 3 significant volumes which current a complete remedy of the idea of the most sessions of certain features from the viewpoint of the speculation of workforce representations. This quantity offers with the homes of targeted capabilities and orthogonal polynomials (Legendre, Gegenbauer, Jacobi, Laguerre, Bessel and others) that are on the topic of the category 1 representations of assorted teams.
Module conception over commutative asociative earrings is mostly prolonged to noncommutative associative jewelry by way of introducing the class of left (or correct) modules. a substitute for this strategy is advised through contemplating bimodules. a elegant module concept for associative jewelry is used to enquire the bimodule constitution of arbitary algebras and workforce activities on those algebras.
"A remarkably intelligible survey . . . good geared up, good written and extremely transparent all through. " — Mathematical ReviewsThis very good textual content, lengthy one in all the best-written, such a lot skillful expositions of workforce concept and its actual functions, is directed essentially to complicated undergraduate and graduate scholars in physics, specially quantum physics.
- The algebraic theory of semigroups
- Symmetry Rules: How Science and Nature are founded on Symmetry (The Frontiers Collection)
- Groups, Combinatorics and Geometry
- Hyperbolic geometry and Algebraic geometry
- Groups of Divisibility
- Spaces of Kleinian Groups
Extra resources for Abelian L-Adic Representations and Elliptic Curves (Advanced Book Classics)
Let v € L , let 1 F. pv and let Fv be the Frobenius conjugacy cla s s of v in Aut( T1 (E» . The eigenvalue s of Fv are algebraic numbe r s ; when embedded into C they give c onjugate c omplex numbe r s / 7rv ;v with 1 7r v I = Nvl 2 . We may write then , 7r = ( Nv ) l / 2 e V -i4J v with 0 < 7r - 4J v - < On the othe r hand, let G = SU( 2 ) be the Lie group of 2 X 2 unitary matric e s with dete rminant 1 . Any element of the spac e X of c onjugacy clas s e s of G contains a unique matrix of the form i4J 0 (e "IP," 0 � 4J � The ima g e in X of the Haar measure of G � 0 e -l� 2 s in 2 4J d4J.
The abelian variety ) ha s "bad r educ tion ", cf . [3 2]. Que stions 1. Let P P be a rational i-adic rep r e s entation. Is it true that v, p ha s rational c o efficients f o r all v such that at v? P i s unraITlified A sOITlewhat s iITlila r que stion i s : I s any c OITlpatibl e sy steITl strictly c OITlpatible? 2. Can any rational i-adic r ep re s entation be obtained (by ten sor p r oduc t s , dir ect SUITlS, etc . ) froITl one s c OITling froITl i-adic c ohoITlology ? 3 . Given a rationa l i-adic r ep r e s entati on p o f K, and a p riITle i' , doe s the r e exist a rational i' -adic r ep r e s e ntation p ' of K c OITlpatible with p?
A . L e t K b e quadr atic ove r 0 , b . T ake for K a c ub ic field with one r e al place and one c om plex one , and l e t again E b e its g roup of units (of r ank 1) . Show that dim T = 3 and diIn T E = 1. T HE GRO UP II- 3 5 m (F or more example s , s e e 3 . 3 . ) 1 . 3 . Enlarg ing g r oup s Let k be a fie ld and A a c ommutative alg eb r aic g r oup ove r k. Le t (* ) o � Y � Y � Y � 0 2 l 3 an exact s e quenc e of (ab s tract) c ommutative group s , with Y 3 finite . Let b e a h o m om o r ph i s m of Y 1 into the g r oup of k - r ational points of A.