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Rational Points and Unipotent Fundamental Groups
Başlık:
Rational Points and Unipotent Fundamental Groups
Yazar:
Hast, Daniel Rayor, author.
ISBN:
9780438019935
Yazar Ek Girişi:
Fiziksel Tanımlama:
1 electronic resource (76 pages)
Genel Not:
Source: Dissertation Abstracts International, Volume: 79-10(E), Section: B.
Advisors: Jordan S. Ellenberg Committee members: Nigel Boston; Autumn E. Kent; Melanie M. Wood.
Özet:
We investigate rational points on higher genus curves over number fields using Kim's non-abelian Chabauty method. We provide an exposition of this method, including a brief survey of the literature in the area. In joint work with Ellenberg, we then study the Selmer varieties of smooth projective curves of genus at least two defined over Q which geometrically dominate a curve with CM Jacobian. We extend a result of Coates and Kim to show that the non-abelian Chabauty method applies to such a curve. By combining this with results of Bogomolov--Tschinkel and Poonen on unramified correspondences, we deduce that any cover of the projective line with solvable Galois group, and in particular any superelliptic curve over Q, has only finitely many rational points over Q.
We also present a strategy for generalizing the non-abelian Chabauty method to real number fields: A conjecture on certain transcendence properties of the unipotent Albanese map is formulated in the final two chapters of this thesis, together with a proof that this conjecture allows a generalization of several major results in the non-abelian Chabauty method to curves over a real number field.
Notlar:
School code: 0262
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Yer Numarası | Demirbaş Numarası | Shelf Location | Lokasyon / Statüsü / İade Tarihi |
---|---|---|---|
XX(682706.1) | 682706-1001 | Proquest E-Tez Koleksiyonu | Arıyor... |
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