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 9 of 9 for “"Abelian variety"”.
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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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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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Arithmetic properties and decomposability of Jacobians
… studying the action of a finite group on an abelian variety in general. Next, we use methods for point counting properties of curves over finite fields to study the decomposability of Jacobians over number fields and finite fields. For example, we show that the genus of curves over number …
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On trigonometric and elliptic Cherednik algebras
… we define the elliptic Dunkl operators on an abelian variety with a finite group action. Using these elliptic Dunkl operators, we construct a new family of quantum integrable systems.
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p-adic Heights of Heegner points on Shimura curves
… by the p-adic height of a Heegner point on the abelian variety A associated to f. This p-adic Gross-Zagier formula generalises the result obtained by Perrin-Riou when F=Q and N satisfies the so-called Heegner condition. We deduce applications to both the p-adic and the classical Birch and …
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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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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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Plectic arithmetic of Hilbert modular varieties
… 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 main result is that the map that sends a point on the …
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Explicit moduli spaces for curves of genus 1 and 2
… elements of the Tate--Shafarevich group of an abelian variety. In particular, we construct a number of genus 2 Jacobians $J/\mathbb{Q}$ with real multiplication by $\mathbb{Z}[\sqrt{2}]$ and whose Tate--Shafarevich groups contain an element of order $7$. Our approach is to find elliptic curves …