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 20 of 24 for “"Abelian varieties"”.
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Degenerating abelian varieties via log abelian varieties
… any given split totally degenerate semi-stable abelian variety over a complete discrete valuation field. Such models are used to construct a log abelian variety over the corresponding discrete valuation ring (endowed with the canonical log structure), which extends the given abelian variety.
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F-virtual Abelian Varieties and Rallis Inner Product Formula
… consists of two topics. First we study F-virtual Abelian varieties of GL2-type where F is a number field. We show the relation between these Abelian varieties and those defined over F. We compare their l-adic representations and study the modularity of F-virtual Abelian varieties of GL2-type. Then …
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Representations of Fundamental Groups of Abelian Varieties in Characteristic P
Let $A_g$ be an abelian variety of dimension $g$ and $p$-rank $\lambda \leq 1$ over an algebraically closed field of characteristic $p>0$. We compute the number of homomorphisms from $\pi_1^{\text{\'et}}(A_g)$ to $GL_n(\mathbb F_q)$, where $q$ is any power of $p$. We show that for fixed $g$, …
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Arboreal representations, sectional monodromy groups, and abelian varieties over finite fields
This thesis consists of three independent parts. The first part studies arboreal representations of Galois groups - an arithmetic dynamics analogue of Tate modules - and proves some large image results, in particular confirming a conjecture of Odoni. Given a field K, a separable polynomial …
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Theta functions and division points on Abelian varieties of dimension two
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1985.
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Langlands Duality in the Generic Fibres of Classical Hitchin Fibrations
… to Hitchin's result, the bres are torsors of abelian varieties, and we demonstrate Langlands duality in the Hitchin bration by proving the generic bres corresponding to Langland's dual groups are indeed dual abelian varieties. The thesis consists of two parts. In Part I, we review the …
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Hyper-Kaehler fibrations and Hilbert schemes
… are fibrations. It is known that the fibers are abelian varieties and the base is P2. We assume that the general fiber is isomorphic to a product of two elliptic curves. We are able to relate this class of hyper-Kähler fibrations to already known examples. We prove that such a hyper-Kähler …
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Low Genus Curves on Compact Shimura Surfaces
… uniform boundedness on the endomorphism types of abelian varieties.
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ABC Theorems In The Functional Case
… order to prove his ABC Theorems for isotrivial abelian varieties, respectively with trace zero. We hope to be able to use these results in order to prove a version of an ABC Theorem for any abelian variety over a function field.
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Siegel modulator form (mod p) and algebraic modular forms
… to the superspecial locus of the moduli space of abelian varieties.
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The blowup formula for higher rank Donaldson invariants
… a formal argument to explain the appearance of Abelian varieties and theta functions in four dimensional topological field theories.
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Singularities of the Perfect Cone Compactification
… of the moduli space of principally polarised abelian varieties, the object taken into consideration consists of the perfect cone (also known as first Voroni) compactification of arithmetic quotients of type IV domains. These are of importance in the context of algebraic geometry because they …
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Topics in categorical algebra and Galois theory
… and discuss their form in particular semi-abelian varieties. We then give a thorough description of categorical Galois theory, which yields an analogue for the fundamental theorem of Galois theory in an abstract category by making use of the notions of admissibility and effective descent. …
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Plectic arithmetic of Hilbert modular varieties
… and on the set of cocharacters of Shimura varieties that differ in the centre from the Hilbert modular variety. By allowing the centre to vary, we extend the plectic framework of Nekovář--Scholl to include such Shimura varieties, thereby also bridging the gap to earlier work of Nekovář. Our …
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Selmer groups as flat cohomology groups
… and Kato showed how the p Selmer group of an abelian variety A over a number field K is determined by the p-adic Tate module. In general, the pm1-Selmer group Selpmn A need not be determined by the mod pm Galois representation A[pm]; we show, however, that this is the case if p is large …
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Counterexamples related to the Sato-Tate conjecture
… $\epsilon>0$. This provides evidence that for CM abelian varieties, the converse to ``Akiyama--Tanigawa conjecture implies generalized Riemann hypothesis'' does not follow in a straightforward way from the standard analytic methods. We also show that there are Galois representations $\rho\colon …
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Computing canonical heights on Jacobians
… tool for the study of the arithmetic of abelian varieties. In this dissertation we investigate methods for the explicit computation of canonical heights on Jacobians of smooth projective curves. Building on an existing algorithm due to Flynn and Smart with modifications by Stoll we …
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