Abstract. 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.
For any "nite "eld k we count the number of orbits of galois invariant n-sets of /(k M ) under the action of PGL (k). For k of odd characteristic, this counts the number of k-points of the moduli space of hyperelliptic curves of genus g over k. We get in this way an explicit formula for the number of hyperelliptic curves over k of genus g, up to k-isomorphism and quadratic twist.2002 Elsevier Science (USA)
Abstract. Let A be an isogeny class of abelian surfaces over Fq with Weil polynomial x 4 +ax 3 +bx 2 +aqx+q 2 . We show that A does not contain a surface that has a principal polarization if and only if a 2 − b = q and b < 0 and all prime divisors of b are congruent to 1 modulo 3.
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