- Library Home /
- Search Collections /
- Open Collections /
- Browse Collections /
- UBC Theses and Dissertations /
- Two special cases of the Dynamical Mordell-Lang Conjecture...
Open Collections
UBC Theses and Dissertations
UBC Theses and Dissertations
Two special cases of the Dynamical Mordell-Lang Conjecture in positive characteristic Nelson, Kristina
Abstract
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 ∈ ℕ, and let G denote the multiplicative group of K, of dimension k. Let α be an element of G, and V a variety contained in G. Let φ: G →G be a group endomorphism defined over K. We know φ(x₁,x₂,...,xk)=(x₁^a1,1 x₂^a1,2 ··· xk^a1k , ... , x₁^ak1 x₂^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 ∈ ℕ double : φ^n(α) ∈ 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 φ.
Item Metadata
Title |
Two special cases of the Dynamical Mordell-Lang Conjecture in positive characteristic
|
Creator | |
Publisher |
University of British Columbia
|
Date Issued |
2017
|
Description |
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 ∈ ℕ, and let G denote the multiplicative group of K, of dimension k. Let α be an element of G, and V a variety contained in G. Let φ: G →G be a group endomorphism defined over K. We know
φ(x₁,x₂,...,xk)=(x₁^a1,1 x₂^a1,2 ··· xk^a1k , ... , x₁^ak1 x₂^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 ∈ ℕ double : φ^n(α) ∈ 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 φ.
|
Genre | |
Type | |
Language |
eng
|
Date Available |
2017-04-12
|
Provider |
Vancouver : University of British Columbia Library
|
Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
|
DOI |
10.14288/1.0343589
|
URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
|
Graduation Date |
2017-05
|
Campus | |
Scholarly Level |
Graduate
|
Rights URI | |
Aggregated Source Repository |
DSpace
|
Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International