Let be a field of odd characteristic , let be an irreducible separable polynomial of degree with big Galois group (the symmetric group or the alternating group). Let be the hyperelliptic curve and its jacobian. We prove that does not have nontrivial endomorphisms over an algebraic closure of if either or .
Soient un corps de caractéristique impaire et un polynôme irréductible séparable dans de degré , avec grand groupe de Galois (le groupe symétrique ou le groupe alterné). Soit la courbe hyperelliptique et sa jacobienne. Nous montrons que n’a pas d’endomorphisme non trivial sur une clôture algébrique de si ou .
Keywords: hyperelliptic jacobians, endomorphisms of abelian varieties, supersingular abelian varieties
Mot clés : jacobiennes hyperelliptiques, endomorphismes des variétés abéliennes, variétés abéliennes supersingulières
@article{BSMF_2004__132_4_617_0, author = {Zarhin, Yuri G.}, title = {Non-supersingular hyperelliptic jacobians}, journal = {Bulletin de la Soci\'et\'e Math\'ematique de France}, pages = {617--634}, publisher = {Soci\'et\'e math\'ematique de France}, volume = {132}, number = {4}, year = {2004}, doi = {10.24033/bsmf.2477}, mrnumber = {2131907}, zbl = {1079.14038}, language = {en}, url = {http://www.numdam.org/articles/10.24033/bsmf.2477/} }
TY - JOUR AU - Zarhin, Yuri G. TI - Non-supersingular hyperelliptic jacobians JO - Bulletin de la Société Mathématique de France PY - 2004 SP - 617 EP - 634 VL - 132 IS - 4 PB - Société mathématique de France UR - http://www.numdam.org/articles/10.24033/bsmf.2477/ DO - 10.24033/bsmf.2477 LA - en ID - BSMF_2004__132_4_617_0 ER -
%0 Journal Article %A Zarhin, Yuri G. %T Non-supersingular hyperelliptic jacobians %J Bulletin de la Société Mathématique de France %D 2004 %P 617-634 %V 132 %N 4 %I Société mathématique de France %U http://www.numdam.org/articles/10.24033/bsmf.2477/ %R 10.24033/bsmf.2477 %G en %F BSMF_2004__132_4_617_0
Zarhin, Yuri G. Non-supersingular hyperelliptic jacobians. Bulletin de la Société Mathématique de France, Volume 132 (2004) no. 4, pp. 617-634. doi : 10.24033/bsmf.2477. http://www.numdam.org/articles/10.24033/bsmf.2477/
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