A comparison of elliptic units in certain prime power conductor cases

Ulrich Schmitt

Displaying similar documents to “A comparison of elliptic units in certain prime power conductor cases”

Iwasawa theory for elliptic curves over imaginary quadratic fields

Massimo Bertolini (2001)

Journal de théorie des nombres de Bordeaux

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Let $E$ be an elliptic curve over $ℚ$ , let $K$ be an imaginary quadratic field, and let $K_{\infty}$ be a $ℤ_{p}$ -extension of $K$ . Given a set $Σ$ of primes of $K$ , containing the primes above $p$ , and the primes of bad reduction for $E$ , write $K_{Σ}$ for the maximal algebraic extension of $K$ which is unramified outside $Σ$ . This paper is devoted to the study of the structure of the cohomology groups $H^{i} (K_{Σ} / K_{\infty}, E_{p^{\infty}})$ for $i = 1, 2,$ and of the $p$ -primary Selmer group Sel $_{p^{\infty}} (E / K_{\infty})$ , viewed as discrete modules over the Iwasawa algebra of $K_{\infty} / K .$ ...

On the Iwasawa theory of CM elliptic curves at supersingular primes

Gary McConnell (1996)

Compositio Mathematica

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A note on integral points on elliptic curves

Mark Watkins (2006)

Journal de Théorie des Nombres de Bordeaux

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We investigate a problem considered by Zagier and Elkies, of finding large integral points on elliptic curves. By writing down a generic polynomial solution and equating coefficients, we are led to suspect four extremal cases that still might have nondegenerate solutions. Each of these cases gives rise to a polynomial system of equations, the first being solved by Elkies in 1988 using the resultant methods of , with there being a unique rational nondegenerate solution. For the second...

A Note on the Uniqueness and Structure of Solutions to the Dirichlet Problem for Some Elliptic Systems

Chern, Jang-Long, Yotsutani, Shoji, Kawano, Nichiro

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In this note, we consider some elliptic systems on a smooth domain of $R^{n}$ . By using the maximum principle, we can get a more general and complete results of the identical property of positive solution pair, and thus classify the structure of all positive solutions depending on the nonlinarities easily.

Elliptic curves over function fields with a large set of integral points

Ricardo P. Conceição (2013)

Acta Arithmetica

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We construct isotrivial and non-isotrivial elliptic curves over $_{q} (t)$ with an arbitrarily large set of separable integral points. As an application of this construction, we prove that there are isotrivial log-general type varieties over $_{q} (t)$ with a Zariski dense set of separable integral points. This provides a counterexample to a natural translation of the Lang-Vojta conjecture to the function field setting. We also show that our main result provides examples of elliptic curves with an explicit...

On the classgroups of imaginary abelian fields

David Solomon (1990)

Annales de l'institut Fourier

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Let $p$ be an odd prime, $χ$ an odd, $p$ -adic Dirichlet character and $K$ the cyclic imaginary extension of $Q$ associated to $χ$ . We define a “ $χ$ -part” of the Sylow $p$ -subgroup of the class group of $K$ and prove a result relating its $p$ -divisibility to that of the generalized Bernoulli number $B_{1, χ^{- 1}}$ . This uses the results of Mazur and Wiles in Iwasawa theory over $Q$ . The more difficult case, in which $p$ divides the order of $χ$ is our chief concern. In this case the result is new and confirms an earlier conjecture...

Lower semicontinuity of variational integrals on elliptic complexes

Anna Verde (2011)

Studia Mathematica

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We prove a lower semicontinuity result for variational integrals associated with a given first order elliptic complex, extending, in this general setting, a well known result in the case $^{'} (ℝ ⁿ, ℝ) \to^{\nabla}' (ℝ ⁿ, ℝ ⁿ) \to^{c u r l}' (ℝ ⁿ, ℝ^{n \times n})$ .

$S$ -integral solutions to a Weierstrass equation

Benjamin M. M. de Weger (1997)

Journal de théorie des nombres de Bordeaux

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The rational solutions with as denominators powers of $2$ to the elliptic diophantine equation $y^{2} = x^{3} - 228 x + 848$ are determined. An idea of Yuri Bilu is applied, which avoids Thue and Thue-Mahler equations, and deduces four-term ( $S$ -) unit equations with special properties, that are solved by linear forms in real and $p$ -adic logarithms.

Regularity for elliptic pairs over $ℂ [[]$

David Raimundo (2013)

Rendiconti del Seminario Matematico della Università di Padova

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L-series and their 2-adic valuations at s = 1 attached to CM elliptic curves

Derong Qiu, Xianke Zhang (2002)

Acta Arithmetica

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Optimal $L^{p}$ -properties of Green’s functions for non-divergence elliptic equations in two dimensions

Gioconda Moscariello, Carlo Sbordone (2005)

Studia Mathematica

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A sharp integrability result for non-negative adjoint solutions to planar non-divergence elliptic equations is proved. A uniform estimate is also given for the Green's function.

A nonlocal elliptic equation in a bounded domain

Piotr Fijałkowski, Bogdan Przeradzki, Robert Stańczy (2004)

Banach Center Publications

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The existence of a positive solution to the Dirichlet boundary value problem for the second order elliptic equation in divergence form $- \sum_{i, j = 1}^{n} D_{i} (a_{i j} D_{j} u) = f (u, \int_{Ω} g (u^{p}))$ , in a bounded domain Ω in ℝⁿ with some growth assumptions on the nonlinear terms f and g is proved. The method based on the Krasnosel’skiĭ Fixed Point Theorem enables us to find many solutions as well.