Jeudi 14 décembre 2017 à 16h00 en salle C48
Édouard Rousseau (UVSQ et Télécom ParisTech)

Titre : Lattices of compatibly embedded finite fields

Résumé :
In this talk, we will discuss the problem of compatibility between finite fields embeddings. Given two finites fields k = GF(p^m) and K = GF(p^n), we know that k can be embedded into K if and only if m divides n. When m = n, this is called the isomorphism problem and we will first give ways of solving this problem. Then, given finite fields k_1, k_2, ..., k_r, we want to be able to create embeddings between them that are compatible. It means that given three finite fields embeddings fA_B from A to B, fB_C from B to C and fA_C from A to C (with A, B, C some fields), we want the composition of fA_B and fB_C to be equal to fA_C. We will give a solution by Bosma, Cannon, and Steel, and implemented in the computer algebra software MAGMA, and we will discuss the possible improvements of their method.