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Uniformity in Polynomial Dynamics: Canonical Heights, Primitive Prime Divisors, and Galois Representations
Başlık:
Uniformity in Polynomial Dynamics: Canonical Heights, Primitive Prime Divisors, and Galois Representations
Yazar:
Looper, Nicole Romain, author.
ISBN:
9780438117167
Yazar Ek Girişi:
Fiziksel Tanımlama:
1 electronic resource (108 pages)
Genel Not:
Source: Dissertation Abstracts International, Volume: 79-11(E), Section: B.
Advisors: Laura G. DeMarco Committee members: Rafe Jones; Bryna R. Kra.
Özet:
In this thesis, we study arithmetic phenomena exhibited by polynomial dynamical systems on the projective line. Specifically, given a number field K, we are interested in the arithmetic of orbits of points alpha∈ K under polynomials &phis; ∈ K[z]. Given such a polynomial &phis; of degree d ≥ 2, we prove a lower bound on the canonical height of any non-preperiodic alpha∈ K. This bound depends only on d, K, and the number of places of bad reduction of &phis;. We then use this result to prove a uniform bound on the sizes of Zsigmondy sets associated to unicritical polynomials defined over a number field, assuming the abc-Conjecture. These theorems illustrate the principle that for a point alpha∈ K having infinite forward orbit under &phis;, we expect the iterates &phis; n(alpha) to exhibit arithmetically generic behavior as n → infinity, in a way that is independent of the particular choices of alpha and &phis;. Finally, we study the arithmetic of critical orbits in families of trinomials, and thereby prove several large image theorems for arboreal representations.
Notlar:
School code: 0163
Konu Başlığı:
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Yer Numarası | Demirbaş Numarası | Shelf Location | Lokasyon / Statüsü / İade Tarihi |
---|---|---|---|
XX(693674.1) | 693674-1001 | Proquest E-Tez Koleksiyonu | Arıyor... |
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