By Jean-Pierre Serre

ISBN-10: 0201093847

ISBN-13: 9780201093841

This vintage publication comprises an advent to platforms of l-adic representations, a subject of serious value in quantity conception and algebraic geometry, as mirrored by way of the fantastic fresh 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). The final bankruptcy handles the case of elliptic curves with out complicated multiplication, the most results of that's that identical to the Galois staff (in the corresponding l-adic illustration) is "large."

Show description

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

Similar algebraic geometry books

Get Computational Commutative Algebra 1 PDF

This creation to polynomial jewelry, Gröbner bases and functions bridges the distance within the literature among conception and genuine computation. It information a variety of purposes, masking fields as disparate as algebraic geometry and fiscal markets. to help in a whole knowing of those purposes, greater than forty tutorials illustrate how the idea can be utilized.

Read e-book online Novikov Conjectures, Index Theorems, and Rigidity PDF

The Novikov Conjecture is the one most vital unsolved challenge within the topology of high-dimensional non-simply attached manifolds. those volumes are the outgrowth of a convention held on the Mathematisches Forschungsinstitut Oberwolfach (Germany) in September, 1993, with regards to `Novikov Conjectures, Index Theorems and Rigidity'.

Get Ramanujan's Lost Notebook PDF

Within the spring of 1976, George Andrews of Pennsylvania kingdom college visited the library at Trinity collage, Cambridge, to ascertain the papers of the overdue G. N. Watson. between those papers, Andrews chanced on a sheaf of 138 pages within the handwriting of Srinivasa Ramanujan. This manuscript used to be quickly detailed, "Ramanujan's misplaced workstation.

Extra info for Abelian l-adic representations and elliptic curves

Example text

Let __A__ be the fraction which corresponds to the p - qz factor p - qz, and let the fraction corresponding to the other factor S be equal to ~, hence, so that, according to section 39, p S ~ A p - qz + p S M (p - qz)S' M - AS Since these two fractions are equal M - AS must be (p - qz)S· divisible by p - qz and the quotient of M - AS by p - qz is equal to the polynomial function P. Since p - qz is a divisor of M - AS, M - AS vanishes when we let z = l!.. Therefore, if we substitute the constant l!..

In the case treated here the total degree of y and z is either m or n. 58. If in the equation giving the relationship between y and z there are three different combined powers, such that, the largest total degree differs from the middie total degree by the same amount as the middle total degree differs from the smallest, then y and z can be expressed in terms of the new variable x by solving a quadratic equation. If we let y = xz and then divide by the least power of z, then z can be expressed in terms of x by means of the quadratic formula.

47. If y = ~, then a new variable x, by which both z and y can be 39 expressed without radicals, is found in the following manner. Since both z and yare to be functions of x, whose expressions are not to contain radicals, it is clear that this can be done if we let ~ = bx. First we have y = bx and y and expressed both y a + bz = b 2 x 2 , so that z z by functions of ~, z becomes bx 2 - 1, so that = bx 2 - 1. Thus we have x without radicals, and since y bx. m + 48. If y = (a bz) n, then a new variable x by means of which y can be expressed without radicals, is found as follows.

Download PDF sample

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


by Donald
4.4

Rated 4.31 of 5 – based on 44 votes