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Progress in Galois Theory

Part of the Developments in Mathematics Book Series (volume 12)

Editors: Voelklein, Helmut; Shaska, Tanush

DOI: 10.1007/b101762

ISBN: 978-0-387-23533-2

Publisher: Springer US - Springer Journals

Jan 1, 2005

1 - 9 of 9 Chapters

LitStream

Chapter 1Supplementary Thoughts on Symplectic Groups

Abhyankar, Shreeram S.; Inglis, Nicholas F. J.; Yalcin, Umud D.

Pages: 1 –23

[Let b be a nondegenerate symplectic form on a vector space V over a finite field. It is well-known that every intermediate group between Sp(V,b) and ΓSp(V,b) (i.e. the isometry and the semisimilarity groups of b, respectively) is Rank 3 in its action on the projective space P(V). We prove that...
LitStream

Chapter 2Automorphisms of the Modular Curve

Bending, Peter; Camina, Alan; Guralnick, Robert

Pages: 25 –37

[Let p>5 be a prime. Let X be the reduction of the modular curve X(p) in characteristic ℓ (with ℓ≠p). Aside from two known cases in characteristic ℓ=3 (with p=7, 11), we show that the full automorphism group of X is PSL(2,p).]
LitStream

Chapter 3Reducing the Fontaine-Mazur Conjecture to Group Theory

Boston, Nigel

Pages: 39 –50

[Galois groups of infinite p-extensions of number fields unramified at p are a complete mystery. We find by computer a family of pro-p groups that satisfy everything that such a Galois group must, and give evidence for the conjecture that these are the only such groups. This suggests that these...
LitStream

Chapter 4Relating Two Genus 0 Problems of John Thompson

Fried, Michael D.

Pages: 51 –85

[Excluding a precise list of groups like alternating, symmetric, cyclic and dihedral, from 1st year algebra (§7.2.3), we expect there are only finitely many monodromy groups of primitive genus 0 covers. Denote this nearly proven genus 0 problem as Problem0g=02. We call the exceptional groups...
LitStream

Chapter 5Relatively Projective Groups as Absolute Galois Groups

Haran, Dan; Jarden, Moshe

Pages: 87 –100

[A group structure G = (G, Gl,..., Gn) is projective if and only if G is isomorphic to a Galois group structure \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}...
LitStream

Chapter 6Invariants of Binary Forms

Krishnamoorthy, Vishwanath; Shaska, Tanush; Völklein, Helmut

Pages: 101 –122

[Basic invariants of binary forms over ℂ up to degree 6 (and lower degrees) were constructed by Clebsch and Bolza in the 19-th century using complicated symbolic calculations. Igusa extended this to algebraically closed fields of any characteristic using difficult techniques of algebraic...
LitStream

Chapter 7Some Classical Views on the Parameters of the Grothendieck-Teichmüller Group

Nakamura, Hiroaki

Pages: 123 –133

[We present two new formulas concerning behaviors of the standard parameters of the Grothendieck-Teichmüller group \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}...
LitStream

Chapter 8The Image of a Hurwitz Space Under the Moduli Map

Völklein, Helmut

Pages: 135 –150
LitStream

Chapter 9Very Simple Representations: Variations on a Theme of Clifford

Zarhin, Yuri G.

Pages: 151 –168

[We discuss a certain class of absolutely irreducible group representations that behave nicely under the restriction to normal subgroups and subalgebras. Interrelations with doubly transitive permutation groups and endomorphisms of hyperelliptic jacobians are discussed.]

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