Now showing items 21-30 of 510
On Icosahedral Artin Representations
(Duke University Press, 2001)
If ρ: Gal(Qac/Q) → GL2(C) is a continuous odd irreducible representation with nonsolvable image, then under certain local hypotheses we prove that is the representation associated to a weight 1 modular form and hence ...
Dynamics on K3 Surfaces: Salem Numbers and Siegel Disks
(Walter de Gruyter, 2002)
This paper presents the first examples of K3 surface automorphisms \(f : X \rightarrow X\) with Siegel disks (domains on which f acts by an irrational rotation). The set of such examples is countable, and the surface \(X\) ...
On the Meromorphic Continuation of Degree Two L-Functions
(Universität Bielefeld, Fakultät für Mathematik, 2006)
We prove that the L-function of any regular (distinct Hodge numbers), irreducible, rank two motive over the rational numbers has meromorphic continuation to the whole complex plane and satisfies the expected functional equation.
Compatibility of Local and Global Langlands Correspondences
(American Mathematical Society, 2007)
We prove the compatibility of local and global Langlands correspondences for \(GL_n\), which was proved up to semisimplification in M. Harris and R. Taylor, The Geometry and Cohomology of Some Simple Shimura Varieties, ...
On Newforms for Split Special Odd Orthogonal Groups
The theory of local newforms has been studied for the group of \(PGL_n\) and recently \(PGSp_4\) and some other groups of small ranks. In this dissertation, we develop a newform theory for generic supercuspidal representations ...
Rational Point Counts for del Pezzo Surfaces over Finite Fields and Coding Theory
The goal of this thesis is to apply an approach due to Elkies to study the distribution of rational point counts for certain families of curves and surfaces over finite fields. A vector space of polynomials over a fixed ...
Moduli of Galois Representations
The theme of this thesis is the study of moduli stacks of representations of an associative algebra, with an eye toward continuous representations of profinite groups such as Galois groups. The central object of study is ...
The Geometry of Hurwitz Space
We explore the geometry of certain special subvarieties of spaces of branched covers which we call the Maroni and Casnati-Ekedahl loci. Our goal is to understand the divisor theory on compactifications of Hurwitz space, ...
Pencils of quadrics and Jacobians of hyperelliptic curves
Using pencils of quadrics, we study a construction of torsors of Jacobians of hyperelliptic curves twice of which is Pic^1. We then use this construction to study the arithmetic invariant theory of the actions of SO2n+1 ...
Entropy, Dimension and Combinatorial Moduli for One-Dimensional Dynamical Systems
The goal of this thesis is to provide a unified framework in which to analyze the dynamics of two seemingly unrelated families of one-dimensional dynamical systems, namely the family of quadratic polynomials and continued ...