# Browse Dissertations and Theses - Mathematics by Contributor "Boston, Nigel"

• (1999)
Having explicitly calculated universal deformations, the next logical question is whether we can calculate deformations with local restrictions. In fact, the ordinary deformation problem is representable, and we explain ...

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• (1998)
The objective of this thesis is to generalize this result to a bigger class of elliptic curves. We are going to generalize Serf's result to the family of elliptic curves with full 2-torsion, i.e. elliptic curves of the ...

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• (2001)
The second part of the thesis is focussed on developing an explicit arithmetic for the Jacobian of certain cubic superelliptic curves. We restrict our attention to curves of the form y3 = f( x). Assuming that f(x) is monic ...

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• (2006)
Finally, we look at some nonabelian, real, Galois extensions K of Q , such that GK(2) is not free but has a free subgroup of index 2. In particular we focus on finite split metacyclic extensions and again we explicitly ...

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• (2006)
We use modular forms to come up with an infinite family of groups that can be realized with just one finite ramifying prime. Namely, we establish that ramQ (GL2( F l)) = 1 for infinitely many primes l and for all primes ...

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• (2002)
Let Nq(g) be the maximal number of rational points a global function field of genus g with constant field Fq can have. Let A(q) = lim sup g→infinity Nqg g . As an application of our results, we improve the best ...

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• (1999)
Let K be a number field, p a rational prime, and S a finite set of primes of K, none of which lies above p. Let K S be the maximal pro-p extension of K unramified outside S, and let GS = Gal(KS/K). In the case K = Q ...

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• (1999)
The only parts that depend on GRH are: (1) In the first result when a nonsolvable image of rho does not the embed in GL2( F7 ); (2) In the second result for p = 5 with wild ramification. I plan to remove the GRH hypothesis ...

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• (2004)
Let p be a prime such that p ≡ -1 mod 8. Let k = (p + 1)/2 and write k = 2mq, q odd. Let S = F2[x]/⟨1 + xk⟩ where F2 is the Galois field of two elements. We identify the binary extended quadratic residue ...

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• (2005)
In this thesis, we first introduce Wiles' method to establish that a Calabi-Yau threefold defined over the field Q with 2-dimensional ℓ-adic cohomology is modular, answering a question of Saito & Yui. Second, we ...

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• (2000)
Along the way, we discuss algorithms to efficiently perform group operations in Jacobians of hyperelliptic curves and methods of finding their orders. We conclude by generalizing some heuristics from the case of genus 1 ...

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• (2004)
We conclude with a preliminary description of some joint work with Nigel Boston on the asymptotic distributions of non-abelian G with respect to the discriminant.

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• (2004)
Chapter 4. Let L/K be a finite dimensional Galois field extension with Galois group G, B the set of normal basis generators for this extension, and C = {gamma ∈ L | gammaB = B}. Then C is a group under multiplication. ...

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• (1995)
We consider a question of describing the one-dimensional P-adic representations that lift a given representation over a finite field of the absolute Galois group of a function field K. In this case, the characterization ...

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