Explicit Construction of Self-Dual Integral Normal Bases for the Square-Root of the Inverse Different
نویسنده
چکیده
Let K be a finite extension of Qp, let L/K be a finite abelian Galois extension of odd degree and let OL be the valuation ring of L. We define AL/K to be the unique fractional OL-ideal with square equal to the inverse different of L/K. For p an odd prime and L/Qp contained in certain cyclotomic extensions, Erez has described integral normal bases for AL/Qp that are self-dual with respect to the trace form. Assuming K/Qp to be unramified we generate odd abelian weakly ramified extensions of K using Lubin-Tate formal groups. We then use Dwork’s exponential power series to explicitly construct self-dual integral normal bases for the square-root of the inverse different in these extensions.
منابع مشابه
Construction of Self-Dual Integral Normal Bases in Abelian Extensions of Finite and Local Fields
Let F/E be a finite Galois extension of fields with abelian Galois group Γ. A self-dual normal basis for F/E is a normal basis with the additional property that TrF/E(g(x), h(x)) = δg,h for g, h ∈ Γ. Bayer-Fluckiger and Lenstra have shown that when char(E) 6= 2, then F admits a self-dual normal basis if and only if [F : E] is odd. If F/E is an extension of finite fields and char(E) = 2, then F ...
متن کاملConstruction of self-dual normal bases and their complexity
Recent work of Pickett has given a construction of self-dual normal bases for extensions of finite fields, whenever they exist. In this article we present these results in an explicit and constructive manner and apply them, through computer search, to identify the lowest complexity of selfdual normal bases for extensions of low degree. Comparisons to similar searches amongst normal bases show t...
متن کاملParameter determination in a parabolic inverse problem in general dimensions
It is well known that the parabolic partial differential equations in two or more space dimensions with overspecified boundary data, feature in the mathematical modeling of many phenomena. In this article, an inverse problem of determining an unknown time-dependent source term of a parabolic equation in general dimensions is considered. Employing some transformations, we change the inverse prob...
متن کاملبررسی bond strength پستD.T. Light به کانال ریشه با کاربرد سیمانهای رزینی dual-cure و self-cure متعاقب شستشو با مواد مختلف
Background and Aim: Nonmetallic tooth- colored posts adhere to canal walls by dentin bonding agents and resin cements. Better retention and proper distribution of stress result from enough and proper bonding. The purpose of this study was to evaluate bond strength of D.T. Light - post with two different resin cements (self-cure & dual-cure) and to investigate the effect of irrigating solutions ...
متن کاملOn the square root of quadratic matrices
Here we present a new approach to calculating the square root of a quadratic matrix. Actually, the purpose of this article is to show how the Cayley-Hamilton theorem may be used to determine an explicit formula for all the square roots of $2times 2$ matrices.
متن کامل