TY - JOUR
T1 - Zeta functions of supersingular curves of genus 2
AU - Maisner, Daniel
AU - Nart, Enric
PY - 2007/1/1
Y1 - 2007/1/1
N2 - We determine which isogeny classes of supersingular abelian surfaces over a finite field k of characteristic 2 contain jacobians. We deal with this problem in a direct way by computing explicitly the zeta function of all supersingular curves of genus 2. Our procedure is constructive, so that we are able to exhibit curves with prescribed zeta function and find formulas for the number of curves, up to k-isomorphism, leading to the same zeta function. © Canadian Mathematical Society 2007.
AB - We determine which isogeny classes of supersingular abelian surfaces over a finite field k of characteristic 2 contain jacobians. We deal with this problem in a direct way by computing explicitly the zeta function of all supersingular curves of genus 2. Our procedure is constructive, so that we are able to exhibit curves with prescribed zeta function and find formulas for the number of curves, up to k-isomorphism, leading to the same zeta function. © Canadian Mathematical Society 2007.
UR - https://www.scopus.com/pages/publications/34248664061
U2 - 10.4153/CJM-2007-016-6
DO - 10.4153/CJM-2007-016-6
M3 - Article
SN - 0008-414X
VL - 59
SP - 372
EP - 392
JO - Canadian Journal of Mathematics
JF - Canadian Journal of Mathematics
ER -