Composite coverings in characteristic p
Abstract
We consider iterates of the generic q-additive polynomial in d variables over various fields which contain the finite field with q-elements. We show that the Galois groups attached to these polynomials are generalized linear groups of d by d matrices. This result provides explicit coverings in the direction of Abhyankar's global and local conjectures related to Galois groups in characteristic p. In addition we deduce an infinite family of infinite groups (matrices over power series rings) as quotients of the total fundamental group. These results are higher dimensional generalizations of a result of Carlitz proved in 1938. The main theorem was motivated by a result of Serre related to Galois groups attached to division points of elliptic curves over $\doubq.$ We present a mild variation of Serre's original proof and this allows us to generalize his theorem to the case of Abelian varieties of any dimension.
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.