Contre-exemples au principe de Hasse pour les courbes de Fermat

Alain Kraus

Acta Arithmetica (2016)

  • Volume: 174, Issue: 2, page 189-197
  • ISSN: 0065-1036

Abstract

top
Let p be an odd prime number. In this paper, we are concerned with the behaviour of Fermat curves defined over ℚ, given by equations a x p + b y p + c z p = 0 , with respect to the local-global Hasse principle. It is conjectured that there exist infinitely many Fermat curves of exponent p which are counterexamples to the Hasse principle. This is a consequence of the abc-conjecture if p ≥ 5. Using a cyclotomic approach due to H. Cohen and Chebotarev’s density theorem, we obtain a partial result towards this conjecture, by proving it for p ≤ 19.

How to cite

top

Alain Kraus. "Contre-exemples au principe de Hasse pour les courbes de Fermat." Acta Arithmetica 174.2 (2016): 189-197. <http://eudml.org/doc/286330>.

@article{AlainKraus2016,
author = {Alain Kraus},
journal = {Acta Arithmetica},
keywords = {Fermat curves; counterexample to the Hasse principle},
language = {fre},
number = {2},
pages = {189-197},
title = {Contre-exemples au principe de Hasse pour les courbes de Fermat},
url = {http://eudml.org/doc/286330},
volume = {174},
year = {2016},
}

TY - JOUR
AU - Alain Kraus
TI - Contre-exemples au principe de Hasse pour les courbes de Fermat
JO - Acta Arithmetica
PY - 2016
VL - 174
IS - 2
SP - 189
EP - 197
LA - fre
KW - Fermat curves; counterexample to the Hasse principle
UR - http://eudml.org/doc/286330
ER -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.