Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 17 of 17 for “"arithmetic geometry"”.
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Number-theoretic properties of the binomial distribution with applications in arithmetic geometry
Alina Bucur et al. showed that the distribution of the number of points on a smooth projective plane curve of degree d over a finite field of order q is approximated by a particular binomial distribution. We generalize their arguments to obtain a similar theorem concerning hypersurfaces in …
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Ensinando integradamente aritmética, geometria e álgebra: propostas de atividades para a matemática do ensino fundamental
… Sequences consist of activities that integrate Arithmetic, Geometry and Algebra Mathematics for the Elementary School. It is an exploratory research, the aims, and as bibliographic data collection. Thus were prepared three Teaching Sequences involving Arithmetic, Algebra and Geometry which …
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Hyperbolic 3-manifolds of bounded volume and trace field degree
… proof of the Bounded Height Conjecture in arithmetic geometry.
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Fourier Coefficients of Modular Forms and Their Applications
… of analytic and algebraic number theory and arithmetic geometry. In this thesis we explore some applications. First, we give some new and simpler proofs of recent results of S.C. Milne, that derive formulas for some infinite families of identities for sums of integer squares. Next, we extend …
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SEMISTABLE MODELS OF HYPERELLIPTIC CURVES IN THE WILD CASE & DIFFERENTIAL OPERATORS ON P-ADIC MODULAR FORMS
… my PhD, both in the realm of number theory and arithmetic geometry. The first part presents a joint work with J. Yelton, regarding semistable models of hyperelliptic curves in the wild case. To this subject, which was already the topic of my MSc. thesis, I devoted part of my research work during …
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Resolução de problemas na matemática: o caso do Município de São Miguel de Itaipu.
… to situations everyday involving the areas of arithmetic, geometry and algebra. We also see the presence of resolution strategies that refer to the same logical structure and organization shown by most students observed. The survey also showed little use of the methodology Troubleshooting …
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An analysis of gender related differences in performance and attitudes of participants in the 1997 UCT Mathematics competition
… of different categories in mathematics (algebra, arithmetic, geometry and problem solving), various sub-categories and special categories; questions that have been repeated in more than one question paper will also be investigated for any patterns in performance (in terms of maturity in …
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Capitulation Discriminants of Genus One Curves
… the curve C with a hyperplane, and use geometry of numbers together with a compactness argument to prove a bound for the capitulation discriminant. For small values of n we then explain how to make this bound e ective. In the second part of the thesis we study Kolyvagin classes in the …
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Lifts of Frobenius on Arithmetic Jet Spaces of Schemes
… of the p-adic integers may be viewed as arithmetic analogues of vector fields on manifolds. In particular, vector fields on the tangent bundle of a manifold, appearing for instance in Hamiltonian mechanics, have as arithmetic analogues lifts of Frobenius on arithmetic jet spaces J^1(X) of …
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Arithmetic Deformation Classes Associated to Curves via p-Jet Spaces
We show that for certain curves over p-adic rings its first p-jet space admits the structure of a torsor under a line bundle.
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Computing the trace of an endomorphism of a supersingular elliptic curve
We provide an explicit algorithm for computing the trace of an endomorphism of an elliptic curve which is given by a chain of small-degree isogenies. We analyze its complexity, determining that if the length of the chain, the degree of the isogenies, and the log of the field-size are all O(n), the …
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SISTEMI, STRUTTURE, SFORZI, MOTI. L¿ANALOGIA TRA SCIENZE FISICO-MATEMATICHE E SCIENZE CIVILI NELLA FILOSOFIA DI G.W. LEIBNIZ
… the respective field of study and application of Arithmetic, Geometry, Mechanics, and Physics? And what kind of relationship exists between them? 3. How are all these sciences (that is, the sciences listed in points 1. and 2.) classified, and how are they related to each other? Which methodologies …
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A Bayesian approach to computing Brauer groups of cubic surfaces
We present an algorithm for computing the Brauer groups of cubic surfaces. The algorithm takes as input an equation for a cubic surface X and a confidence threshold 0.5 < r < 1 and outputs a candidate for the Brauer group of X and a confidence level > r for the result. The algorithm runs by …
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Explicit moduli spaces for curves of genus 1 and 2
… to a power of $r$. We first study the birational geometry of the surfaces $Z_{N,r}^{\text{sym}}$ which arise as quotients of the surfaces $Z_{N,r}$ by the involution swapping the roles of the $N$-congruent elliptic curves. Building on previous work of Kani--Schanz and Hermann we compute the …
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Arithmetical, geometrical, and categorical forays into particle physics
This Thesis will focus on three different forays into particle physics using pure mathematics. Our first foray studies anomaly free gauge algebras. Using geometric methods, we reproduce a solution given to the anomaly cancellation conditions associated with a pure u(1)-gauge theory in Costa et al. …
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Arithmetic statistics and Vinberg representations
In this thesis, we obtain results in arithmetic statistics through Vinberg representations. Very often, the rational and integral orbits of Vinberg representations encode information about certain arithmetic objects of interest. In view of that, we can use Bhargava's techniques in …
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Components of the Emerton-Gee Moduli Stack of Galois Representations for GL2 and A Graph-Theoretic Approach to Computing Selmer Groups of Elliptic Curves over Q(i)
… first part of this thesis, we study the local geometry of the irreducible components in the reduced part of the Emerton–Gee stack for GL_2, which serves as a moduli space for two-dimensional mod p representations of Gal(K/K). We determine precisely which irreducible components are smooth, which …