An Introduction to Algebraic Geometry and Algebraic Groups by Meinolf Geck PDF

By Meinolf Geck

ISBN-10: 019967616X

ISBN-13: 9780199676163

An available textual content introducing algebraic geometries and algebraic teams at complex undergraduate and early graduate point, this booklet develops the language of algebraic geometry from scratch and makes use of it to establish the idea of affine algebraic teams from first principles.

Building at the historical past fabric from algebraic geometry and algebraic teams, the textual content offers an advent to extra complex and specialized fabric. An instance is the illustration concept of finite teams of Lie type.

The textual content covers the conjugacy of Borel subgroups and maximal tori, the speculation of algebraic teams with a BN-pair, a radical therapy of Frobenius maps on affine kinds and algebraic teams, zeta capabilities and Lefschetz numbers for types over finite fields. specialists within the box will take pleasure in the various new methods to classical results.

The textual content makes use of algebraic teams because the major examples, together with labored out examples, instructive routines, in addition to bibliographical and old comments.

Show description

Read Online or Download An Introduction to Algebraic Geometry and Algebraic Groups PDF

Similar algebraic geometry books

Lectures on moduli of curves by D. Gieseker PDF

Those notes are according to a few lectures given at TIFR in the course of January and February 1980. the item of the lectures was once to build a projectire moduli area for good curves of genus g >= 2 utilizing Mumford's geometric' invariant thought.

Haruzo Hida's p-Adic Automorphic Forms on Shimura Varieties PDF

This e-book covers the next 3 issues in a way obtainable to graduate scholars who've an knowing of algebraic quantity conception and scheme theoretic algebraic geometry:1. An straight forward development of Shimura kinds as moduli of abelian schemes. 2. p-adic deformation idea of automorphic types on Shimura forms.

Download e-book for kindle: Records: Mathematical Theory by Valery B. Nevzorov

Drawing seriously from his personal classes on order facts and documents, Nevzorov (mathematics and mechanics, St. Petersburg U. ) bargains introduces the speculation of documents to scholars with simply commonplace classes on likelihood concept and mathematical data. He means that the tools for studying documents, the various list versions, and a number of the purposes he describes might be utilized by engineers and pros in different fields that use facts in addition to via mathematicians.

New PDF release: An Introduction to Algebraic Geometry and Algebraic Groups

An available textual content introducing algebraic geometries and algebraic teams at complex undergraduate and early graduate point, this ebook develops the language of algebraic geometry from scratch and makes use of it to establish the speculation of affine algebraic teams from first principles.

Building at the historical past fabric from algebraic geometry and algebraic teams, the textual content offers an creation to extra complicated and specialized fabric. An instance is the illustration idea of finite teams of Lie type.

The textual content covers the conjugacy of Borel subgroups and maximal tori, the idea of algebraic teams with a BN-pair, an intensive remedy of Frobenius maps on affine types and algebraic teams, zeta services and Lefschetz numbers for forms over finite fields. specialists within the box will take pleasure in a few of the new methods to classical results.

The textual content makes use of algebraic teams because the major examples, together with labored out examples, instructive routines, in addition to bibliographical and ancient comments.

Additional info for An Introduction to Algebraic Geometry and Algebraic Groups

Sample text

Xn ] is such that [f] = 0 (if R = K) or f = 1 (if R = A). Let N := max {deg(f), deg(fi )} and consider the polynomial ring k[Y1 , . . , Yr ]. For any s 0, we construct an injective map β : k[Y1 , . . , Yr ] s → k[X1 , . . , Xn ] Ns /I Ns . This is done as follows. Let g ∈ k[Y1 , . . , Yr ] s . It is readily checked that we have f s g(f1 /f, . . , fr /f) ∈ k[X1 , . . , Xn ] Ns . Then we define β(g) to be the class of f s g(f1 /f, . . , fr /f) modulo I Ns . To show that β is injective, suppose g is such that f s g(f1 /f, .

First note that taking the determinant of Atr QA = Q and using that det(Q) = 0, we obtain det(A) = ±1. Next, if A, B ∈ Γn (Q, k), then we also have AB and A−1 ∈ Γn (Q, k). Finally, writing out the equation Atr QA = Q for all matrix entries, we see that Γn (Q, k) (2) is a closed subset of Mn (k). Thus, Γn (Q, k) ⊆ SLn (k) is a linear algebraic group, called a classical group. If Q ∈ Mn (k) is another invertible matrix, we say that Q, Q are equivalent if there exists some invertible matrix R ∈ Mn (k) such that Q = Rtr QR.

Am ∈ A is algebraically independent if there exists no non-zero polynomial F ∈ k[X1 , . . , Xm ] such that F (a1 , . . , am ) = 0. We set ∂k (A) := sup m 0 there exist m algebraically independent elements in A . If A is a field, then ∂k (A) is called the transcendence degree of A over k. 12 for some properties of ∂k (A). 18 Proposition Let A = k[X1 , . . , Xn ]/I where I ⊆ k[X1 , . . , Xn ] is a proper ideal. Then deg a HPI (t) = ∂k (A). If, moreover, A is an integral domain and K is the field of fractions of A, then deg a HPI (t) = ∂k (A) = ∂k (K).

Download PDF sample

An Introduction to Algebraic Geometry and Algebraic Groups by Meinolf Geck


by Daniel
4.0

Rated 4.48 of 5 – based on 28 votes