Abstracts Category : Other

Two special cases of the Dynamical Mordell-Lang Conjecture in positive characteristic

by Kristina Nelson

We prove the positive characteristic version of the Dynamical Mordell-Lang Conjecture in two novel cases. Let p be a prime and K a field of characteristic p>0. Let k , and let G denote the multiplicative group of K, of dimension k. Let be an element of G, and V a variety contained in G. Let : G G be a group endomorphism defined over K. We know(x,x,...,xk)=(x^a1,1 x^a1,2 xk^a1k , ... , x^ak1 x^ak2 xk^akk),for some integer exponents aij. In the case where the matrix of exponents, ( aij ) is similar to a single Jordan block, we show that the set S = { n double : ^n() V } is a finite union of arithmetic progressions. When the dimension k = 3, we show S is a finite union of arithmetic progressions for any group endomorphism .