Helmut Voelklein, Tanush Shaska's Progress in Galois Theory: Proceedings of John Thompson's PDF

By Helmut Voelklein, Tanush Shaska

ISBN-10: 0387235337

ISBN-13: 9780387235332

The subject matter of this e-book is the interactions among staff thought and algebra/geometry/number idea, exhibiting ubiquity and tool of the elemental precept of Galois idea. The books provides fresh advancements in an incredible line of labor approximately covers of the projective line (and different curves), their fields of definition and parameter areas, and linked questions on mathematics basic teams. this can be in detail tied up with the Inverse challenge of Galois thought, and makes use of tools of algebraic geometry, staff conception and quantity conception.

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Extra resources for Progress in Galois Theory: Proceedings of John Thompson's 70th Birthday Conference

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What is it? There are algebras arising in other areas of mathematics whose graded pieces have the same dimensions, namely (i) the free Lie algebra generated by one generator in degree 1 and one in degree 2 (arising in work on multi-zeta values and quantum field theory [8]) and (ii) Cameron's permutation group algebra [12] of C2 M, where A is the group of all orderpreserving penmitations of the rationals. This suggests the following amazing possibility. Conjecture 4. If G is in the family ^ , then L{G) is the F;,-Lie algebra in (i) or (ii) above.

25-37 H. Voelklein and T. Shaska, Editors ©2005 Springer Science + Business Media, Inc. AUTOMORPHISMS OF THE M O D U L A R CURVE Automorphisms of the modular curve X[p) in positive characteristic For John Thompson on the occasion of his seventieth birthday Peter Bending GCHQ, Priors Road, Cheltenham, Glos, GL52 5AJ, UK. uk Alan Camina School of Mathematics, University of East Anglia, Norwich, England, NR4 IT J, UK. uk Robert Guralnick* Department of Mathematics, University of Southern California, Los Angeles, CA, 90089.

One can prove a weaker result without the classification - for example one can show that large primes cannot divide the order of the full automorphism group, but we do not see how to prove the fiill result without the classification. The fact that M\ \ does come up shows that one does need to loiow facts about simple groups. In fact, Ritzenhaler [Rit] did use the classification as well (but in that case, one can likely avoid its use). We note that the only properties of the modular curve we use are that it admits an action of PSL{2^p) with specified ramification data.

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Progress in Galois Theory: Proceedings of John Thompson's 70th Birthday Conference by Helmut Voelklein, Tanush Shaska

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