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Showing 1 to 12 of 12 for “"Selmer groups"”.
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Selmer groups as flat cohomology groups
… prime number p, Bloch 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 …
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On Selmer groups and factoring p-adic L-functions
… p-adic L-function. We prove a result involving Selmer groups that along with Dasgupta's result is consistent with the main conjectures associated to the 4-dimensional representation (to which the 3-variable p-adic L-function is associated), the 3-dimensional representation (to which the …
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On the Selmer groups of elliptic curves in quadratic twist families
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1995.
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Distribution of Selmer Groups of Quadratic Twists of a Family of Elliptic Curves
… we study the distribution of the size of the six Selmer groups arising from the three 2-isogenies and their dual 2-isogenies. We also describe explicit formulas on the size of the six Selmer groups.
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The Average Size of 2-Selmer Groups of Elliptic Curves in Characteristic 2
… We prove that the average size of the 2-Selmer groups of elliptic curves E/K is at most 1 + 2ζʙ(2)ζʙ(10), where ζʙ is the zeta function of B. In particular, in the limit as q = #k ! ∞ (with the genus g(B) fixed), we see that the average size of 2-Selmer is bounded above by 3, even 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)
… a graph-theoretic algorithm to compute the φ-Selmer group of the elliptic curve E_b : y^2 = x^3 + bx defined over Q(i), where b ∈ Z[i] and φ is a degree 2 isogeny of E_b. We begin by associating a weighted graph G_b to each curve E_b, whose vertices correspond to the odd Gaussian primes …
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Iwasawa theory for modular forms at supersingular primes
… generate the characteristic ideals of some \pm-Selmer groups which are cotorsion over the Iwasawa algebra \Lambda=Zp[[Zp]]. We begin by studying the p-adic Hodge theory for the p-adic representation associated to f in the case when a_p=0. It allows us to give analogous definitions of Kobayashi's …
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On congruence function fields with many rational places
… of function fields. The third part concerns Selmer groups of elliptic curves over the rational function field. Let $\mathcal{H}$ be the Hermitian function field, and $\mathcal{C}$ be a maximal function field, both over the same finite field. In the first part of this thesis, we analyze the …
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First explicit reciprocity law for unitary Friedberg—Jacquet periods
… and Darmon introduced a new technique to bound Selmer groups of elliptic curves via level raising congruences. This was the first example of what is now termed a "bipartite Euler system", and over the last decade we have seen many breakthroughs on constructing such systems for other Galois …
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On the slope filtration of [phi]-modules over the Robba ring
… expected to intervene in the duality theory for Selmer groups associated to de Rham representations. We introduce the notion of families of [phi]-modules which arises naturally from both rigid cohomology and p-adic Hodge theory. We then prove the local constancy of generic HN-polygons of families …
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Iwasawa theory over solvable three-dimensional p-adic Lie extensions
… himself) involved the behaviour of ideal class groups over cyclotomic Zp-extensions, and related this to the Kubota-Leopoldt p-adic zeta-function. During the last two decades, the main conjecture has been greatly generalized to admissible p-adic Lie extensions, and provides a conjectural …
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Arithmetic statistics and Vinberg representations
… results on the average size of some isogeny Selmer groups. The parametrisations arise from the $B$ and $C$ Dynkin diagrams, and are new in the literature. We also observe that some of our average sizes diverge: this is related to the behaviour of a product of Tamagawa ratios arising from a …