Concept

Algebraic number theory

Related publications (38)

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Hermitian Forms over Algebras with Involution and Hermitian Categories

Daniel Arnold Moldovan

This thesis is concerned with the algebraic theory of hermitian forms. It is organized in two parts. The first, consisting of the first two chapters, deals with some descent properties of unimodular hermitian forms over central simple algebras with involut ...

EPFL2012

Primeless Modular Cryptography (Extended Abstract)

Serge Vaudenay, Sonia Mihaela Bogos

Most of the known public-key cryptosystems have an overall complexity which is dominated by the key-production algorithm, which requires the generation of prime numbers. This is most inconvenient in settings where the key-generation is not an one-off proce ...

2012

What are the Longest Ropes on the Unit Sphere?

Henryk Gerlach

We consider the variational problem of finding the longest closed curves of given minimal thickness on the unit sphere. After establishing the existence of solutions for any given thickness between 0 and 1, we explicitly construct for each given thickness ...

Springer-Verlag2011

A general framework for homotopic descent and codescent

Kathryn Hess Bellwald

In this paper we elaborate a general homotopy-theoretic framework in which to study problems of descent and completion and of their duals, codescent and cocompletion. Our approach to homotopic (co)descent and to derived (co)completion can be viewed as $\in ...

2010

Annihilating Polynomials for Quadratic Forms

Klaas-Tido Rühl

Let K be a field with char(K) ≠ 2. The Witt-Grothendieck ring (K) and the Witt ring W (K) of K are both quotients of the group ring ℤ[𝓖(K)], where 𝓖(K) := K*/(K*)2 is the square class group of K. Since ℤ[𝓖(K)] is integra ...

EPFL2010

Construction Of Self-Dual Integral Normal Bases In Abelian Extensions Of Finite And Local Fields

Erik Jarl Pickett

Let

F/E

be a finite Galois extension of fields with abelian Galois group

\Gamma

. A self-dual normal basis for

F/E

is a normal basis with the additional property that

Tr_{F/E}(g(x),h(x))=\delta_{g,h}

for

g,h\in\Gamma

. Bayer-Fluckiger and Lenstra h ...

2010

Explicit construction of self-dual integral normal bases for the square-root of the inverse different

Erik Jarl Pickett

Let K be a finite extension of Q(p), let L/K be a finite abelian Galois extension of odd degree and let D-L be the valuation ring of L. We define A(L/K) to be the unique fractional D-L-ideal with square equal to the inverse different of L/K. For p an odd p ...

2009

Two variants of the support problem for products of abelian varieties and tori

Antonella Perucca

Let G be the product of an abelian variety and a torus defined over a number field K. Let P and Q be K-rational points on G. Suppose that for all but finitely many primes p of K the order of (Q mod p) divides the order of (P mod p). Then there exist a K-en ...

2009

Upper bounds for Euclidean minima of algebraic number fields

Eva Bayer Fluckiger

The aim of this paper is to give new upper bounds for Euclidean minima of algebraic number fields. In particular, to show that Minkowski's conjecture holds for the maximal totally real subfields of cyclotomic fields of prime power conductor. ...

2006

Algebraic methods for channel coding

Frédérique Oggier

This work is dedicated to developing algebraic methods for channel coding. Its goal is to show that in different contexts, namely single-antenna Rayleigh fading channels, coherent and non-coherent MIMO channels, algebraic techniques can provide useful tool ...

EPFL2005

Construction Of Self-Dual Integral Normal Bases In Abelian Extensions Of Finite And Local Fields

Erik Jarl Pickett

Let

F/E

be a finite Galois extension of fields with abelian Galois group

\Gamma

. A self-dual normal basis for

F/E

is a normal basis with the additional property that

Tr_{F/E}(g(x),h(x))=\delta_{g,h}

for

g,h\in\Gamma

. Bayer-Fluckiger and Lenstra h ...

2010