Algebraic Groups and Class Fields by Jean-Pierre Serre

By Jean-Pierre Serre

Precis of the most Results.- Algebraic Curves.- Maps From a Curve to a Commutative Group.- Singular Algebraic Curves.- Generalized Jacobians.- category box Theory.- workforce Extension and Cohomology.- Bibliography.- Supplementary Bibliography.- Index.

Show description

Read or Download Algebraic Groups and Class Fields PDF

Similar abstract books

A Radical Approach to Lebesgue's Theory of Integration (Mathematical Association of America Textbooks)

This full of life advent to degree thought and Lebesgue integration is prompted through the historic questions that resulted in its improvement. the writer stresses the unique objective of the definitions and theorems, highlighting the problems mathematicians encountered as those rules have been sophisticated. the tale starts with Riemann's definition of the indispensable, after which follows the efforts of these who wrestled with the problems inherent in it, until eventually Lebesgue ultimately broke with Riemann's definition.

Fundamentals of Group Theory: An Advanced Approach

<div style="MARGIN: 0in 0in 0pt"><em><span style="COLOR: black">Fundamentals of team idea </span></em><span style="COLOR: black">provides a complete account of the fundamental conception of teams. either vintage and exact issues within the box are lined, akin to an old examine how Galois considered teams, a dialogue of commutator and Sylow subgroups, and a presentation of Birkhoff’s theorem.

Uniqueness and Non-Uniqueness of Semigroups Generated by Singular Diffusion Operators

This publication addresses either probabilists engaged on diffusion approaches and analysts drawn to linear parabolic partial differential equations with singular coefficients. The important query mentioned is whether or not a given diffusion operator, i. e. , a moment order linear differential operator with no zeroth order time period, that's a priori outlined on try capabilities over a few (finite or endless dimensional) nation area basically, uniquely determines a strongly non-stop semigroup on a corresponding weighted Lp house.

Lie Algebras, Cohomology, and New Applications to Quantum Mechanics: Ams Special Session on Lie Algebras, Cohomology, and New Applications to Quantu

This quantity is dedicated to a number of very important new principles coming up within the purposes of Lie teams and Lie algebras to Schrödinger operators and linked quantum mechanical platforms. In those functions, the gang doesn't look as a general symmetry crew, yet fairly as a "hidden" symmetry team whose illustration conception can nonetheless be hired to investigate at least a part of the spectrum of the operator.

Additional resources for Algebraic Groups and Class Fields

Example text

13). 8. Proof in characteristic p > 0: case a) We are going to need the following two elementary lemmas: Lemma 6. Every regular map from the projective line minus one point to the multiplicative group G m is constant. PROOF. We can suppose that the point in question is the point at infinity. , a constant. 0 Lemma 7. Let V be a non-singular variety and let Q be the sheaf of differential forms of degree 1 (cf chap. II, no. 7). Suppose that, for every P E V, the Op-module Q p is generated by elements of HO(V, Q).

H == 1 mod ml on SI - pl. S = = L L p .... P' (110 1I',h)p (110 1I',g)p. o 33 §1. Local symbols 3. Example of a local symbol: additive group case From now on, we limit ourselves to the case where the commutative group G is a connected algebraic group, the map I : X - S -+ G being a regular map. We can then consider I as a rational map from X to G, regular away from S. Unless otherwise stated, we suppose that S is the smallest subset of X having this property, in other words it is the set of points where I is not regular.

Elements The ring A is a k-algebra which is generated by a finite number of Xl, ... ,x n . These elements are integral over A", as the equation 49 §3. Auxiliary results of integral dependence II (x - x") = 0 "Eg shows. The following lemma then shows that A g is a k-algebra of finite type: Lemma 10. Let A be an algebra of finite type over a commutative Noetherian ring k and let B be a subalgebra of A such that every element of A is integral over B. Then B is a k-algebra of finite type. PROOF. Let Xi, 1 :::; i :::; n, be generators of the algebra A; each of these elements satisfies an equation of integral dependence over B, say fi (Xi) = O.

Download PDF sample

Rated 4.62 of 5 – based on 41 votes