Galois theory on the line in nonzero characteristic

The author surveys Galois theory of function fields with non-zero caracteristic and its relation to the structure of finite permutation groups and matrix groups.Comment: 66 pages. Abstract added in migration

Similarity method for the Jacobian problem

This is an expository article giving a modified version of my talk at the October 2006 Conference in Hanoi

Nice equations for nice groups

Nice trinomial equations are given for unramified coverings of the affine line in nonzero characteristicp with PSL(m,q) and SL(m,q) as Galois groups. Likewise, nice trinomial equations are given for unramified coverings of the (once) punctured affine line in nonzero characteristic p with PGL(m,q) and GL(m,q) as Galois groups. Here m>1 is any integer and q>1 is any power of p

Some thoughts on the Jacobian Conjecture, Part II

AbstractIn Abhyankar's Purdue Lectures of 1971, the bivariate Jacobian Conjecture was settled for the case of two plus epsilon characteristic pairs. In the published version, the epsilon part got left out. Now we take care of the omission by preparing for a sharper result with full proof in Part III. The Jacobian Method is applied to giving a new simple proof of Jung's Automorphism Theorem. A detailed description of the Degreewise Newton Polygon is given. Some thoughts on the multivariate Jacobian Conjecture are included

Galois theory of special trinomials

This is the material which I presented at the 60th birthday conference of my good friend Jose Luis Vicente in Seville in September 2001. It is based on the nine lectures, now called sections, which were given by me at Purdue in Spring 1997. This should provide a good calculational background for the Galois theory of vectorial (= additive) polynomials and their iterates