Unramified coverings of the affine line in small positive characteristic
Abstract
We obtain various polynomial equations giving unramified covering of the affine line in characteristics two and three, with alternating groups and Mathieu groups as Galois groups. To compute the Galois groups, we prove several irreducibility lemmas for various polynomials using ramification theory and resolution of singularities of plane curves. Also we develop a few techniques to get upper bounds for the Galois groups. Among them is the linearization process. We connect it with the concept of error correcting codes. Along the way, we discuss how we found those equations using computer programming.
Degree
Ph.D.
Advisors
Abhyankar, Purdue University.
Subject Area
Mathematics
Off-Campus Purdue Users:
To access this dissertation, please log in to our
proxy server.