关于超奇异Weil多项式的奇偶性
On the parity of supersingular Weil polynomials
摘要：
设q是素数p的奇次幂，A/Fq是g维超奇异阿贝尔簇.证明了当p>2g+1时，q-Frobenius的特征多项式是偶多项式.这推广了Fp上超奇椭圆曲线当p>3时p-Frobenius迹为零的著名结果.
英文摘要：
Let q be an odd power of a prime p and let A/Fq be a supersingular abelian variety of dimension g. We show that if p>2g+1, then the characteristic polynomial of the q-Frobenius is an even polynomial. This generalizes the well-known result on the vanishing of the trace of the p-Frobenius when p>3 for supersingular elliptic curves over Fp.
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