Most searched books

Archives

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.- staff Extension and Cohomology.- Bibliography.- Supplementary Bibliography.- Index.

Show description

Read Online or Download Algebraic Groups and Class Fields PDF

Similar abstract books

Function Algebras on Finite Sets. A Basic Course on Many-Valued Logic and Clone Theory

Functionality Algebras on Finite units supplies a extensive creation to the topic, prime as much as the leading edge of analysis. the overall options of the common Algebra are given within the first a part of the publication, to familiarize the reader from the very starting on with the algebraic facet of functionality algebras.

Real Numbers, Generalizations of the Reals, and Theories of Continua

Due to the fact their visual appeal within the overdue nineteenth century, the Cantor--Dedekind thought of actual numbers and philosophy of the continuum have emerged as pillars of ordinary mathematical philosophy. however, this era additionally witnessed the emergence of a number of replacement theories of genuine numbers and corresponding theories of continua, in addition to non-Archimedean geometry, non-standard research, and a few vital generalizations of the method of genuine numbers, a few of that have been defined as mathematics continua of 1 variety or one other.

Axiomatic Method and Category Theory

This quantity explores the numerous diverse meanings of the concept of the axiomatic procedure, supplying an insightful historic and philosophical dialogue approximately how those notions replaced over the millennia. the writer, a widely known thinker and historian of arithmetic, first examines Euclid, who's thought of the daddy of the axiomatic approach, ahead of relocating onto Hilbert and Lawvere.

Abstract harmonic analysis, v.1. Structure of topological groups. Integration theory

Once we acce pted th ekindinvitationof Prof. Dr. F. okay. Scnxmrrto write a monographon summary harmonic research for the Grundlehren. der Maihemaiischen Wissenscha/ten series,weintendedto writeall that wecouldfindoutaboutthesubjectin a textof approximately 600printedpages. We meant thatour e-book could be accessi ble tobeginners,and we was hoping to makeit usefulto experts in addition.

Additional resources for Algebraic Groups and Class Fields

Sample text

If w denotes an inv(lriant differential form on G, then (f + g)*(w) = f*(w) + g*(w). 48 III. Maps From a Curve to a Commutative Group PROOF. Denote by prl and pr2 the two projections of the group G x G to G and put p = prl + pr2. Since G is Abelian these maps are homomorphisms and the differentials p"(w), pri(w) and pr;(w) are invariant differentials on G x G. (w) + pr;(w), this equality is true everywhere. Let (I, g) : X by the pair (I, g). (w) + (I,g)*pr;(w) = f*(w) + g*(w). o 12. Quotient of a variety by a finite group of automorphisms Let V be an algebraic variety and let R be an equivalence relation on V.

If 9 is not constant, (h) (gh - (g) 00 , whence f«h)) 1'(1) - 1'( 00) 0, as was to be shown. 0 = = = = = = 6. Proof in characteristic 0 Let, as before, f : X - S - G be a regular map from X - S to the commutative algebraic group G. Denote by r the dimension of G and let {W1, ... , w r } be a basis of the vector space of differential forms of degree 1 invariant by translation on G (for the properties ofthese forms, cf. no. ll). *(Wi) 1 ~ i ~ r; the O:i are the pull-backs of the Wi by f, and are thus regular on X - S.

It is interesting to note that this proof figures in the work of Chevalley [15] already cited, but not in that of Wei I [88]. As we have seen, the residue formula plays an essential role in identifying differentials with linear forms on repartitions (the "duality" theorem). The first proof of this formula (over a field of any characteristic) is due to Hasse [32]; it is essentially his proof that we have given. The work of Chevalley [15] contains another, rather indirect, but avoiding the difficult lemma 5 (see also Lang [51], chap.

Download PDF sample

Rated 4.09 of 5 – based on 35 votes

Comments are closed.