By Jean-Pierre Serre

ISBN-10: 0201093847

ISBN-13: 9780201093841

This vintage e-book includes an creation to structures of l-adic representations, a subject matter of significant value in quantity conception and algebraic geometry, as mirrored via the excellent contemporary advancements at the Taniyama-Weil conjecture and Fermat's final Theorem. The preliminary chapters are dedicated to the Abelian case (complex multiplication), the place one unearths a pleasant correspondence among the l-adic representations and the linear representations of a few algebraic teams (now referred to as Taniyama groups). The final bankruptcy handles the case of elliptic curves with out advanced multiplication, the most results of that's that clone of the Galois team (in the corresponding l-adic illustration) is "large."

**Read Online or Download Abelian l-adic representations and elliptic curves PDF**

**Similar algebraic geometry books**

**Download e-book for kindle: Abelian l-adic representations and elliptic curves by Jean-Pierre Serre**

This vintage booklet comprises an advent to platforms of l-adic representations, an issue of serious value in quantity thought and algebraic geometry, as mirrored by way of the fabulous contemporary advancements at the Taniyama-Weil conjecture and Fermat's final Theorem. The preliminary chapters are dedicated to the Abelian case (complex multiplication), the place one reveals a pleasant correspondence among the l-adic representations and the linear representations of a few algebraic teams (now known as Taniyama groups).

**Download e-book for kindle: Selected topics in algebraic geometry by Virgil Snyder**

This ebook resulted from experiences (published in 1928 and 1932) of the Committee on Rational differences, demonstrated by way of the nationwide study Council. the aim of the studies was once to provide a accomplished survey of the literature at the topic. every one bankruptcy is considered a separate unit that may be learn independently.

This booklet is dedicated to contemporary development within the research of curves and abelian forms. It discusses either classical elements of this deep and gorgeous topic in addition to vital new advancements, tropical geometry and the speculation of log schemes. as well as unique learn articles, this e-book comprises 3 surveys dedicated to singularities of theta divisors, of compactified Jacobians of singular curves, and of ""strange duality"" between moduli areas of vector bundles on algebraic forms

This ebook offers a self-contained, obtainable creation to the mathematical advances and demanding situations as a result of using semidefinite programming in polynomial optimization. This fast evolving examine sector with contributions from the various fields of convex geometry, algebraic geometry, and optimization is named convex algebraic geometry.

- Tropical Geometry and Mirror Symmetry
- Appendix: The Theory of Space
- Homotopy Invariant Algebraic Structures: A Conference in Honor of Mike Boardman : Ams Special Session on Homotopy Theory, January 1998, Baltimore, MD
- Elliptic curves, modular forms, and their L-functions

**Additional resources for Abelian l-adic representations and elliptic curves**

**Sample text**

N -1 and fi = i = 0, .. ,n (as power series). it, i Zi = Zi, Proof. 11). The conclusion of the proposition is equivalent to the assertion that F must be the identity map of C. By definition F is a complex analytic automorphism of C, that is, a projective transformation. 13) F 0 -1 IBmin(ro,ro). 15) for some nonzero complex number a. 15) we have lim wfo w-+O Since fo is of the form w+ (W) = 1. 16) implies a = 1. Thus F is the identity map of C. 4. 5. 4. 26 1. 17) is called a canonical sphere with tubes of type (1,0).

Though in this work we do not need that proof, the idea and the method used in that proof might be useful for further studies, especially of the maps E and E- 1 • Also, that proof involves some interesting formal calculus and is related to formal groups. So here we give the heuristic idea of that proof and leave the rigorization to the reader as an exercise. L. 00 3=30 F(z) = J (E:-1(a)) . ~l E·30 (a) Z3+1, gtz)dZ. 1. FORMAL POWER SERIES AND EXPONENTIALS OF DERIVATIONS 43 g (exp (Eio1(a):) F-l(y») j y y=F(",) = g(p-l(y + Eio1(a)))\y=F(",) = = exp (Eio1(a): ) y g(F-1(y»j y=F(",) = e1/(:C)g(:c).

I " (z). ml···mn ,A,ao ml···m .. t,{. )) = eA(' )a: d. 4). 2. From the above proposition we see that heuristically the composition (f~') )-' C~{. )) is generated by the "formal infinitesimal conformal transformations" This composition is a formal analogue of the right-hand side of the sewing equation or the "formal transition map" of a sphere with tubes sewn from two canonical spheres with tubes (see Chapters 1). This is the reason why we construct the "formal conformal transformations" from the "formal infinitesimal conformal transformations" in this way.

### Abelian l-adic representations and elliptic curves by Jean-Pierre Serre

by John

4.4