Hyperelliptic curves over $\mathbb{F}_2$ of every $2$-rank without extra automorphisms
نویسندگان
چکیده
منابع مشابه
Hyperelliptic Curves over F2 of Every 2-rank without Extra Automorphisms
We prove that for any pair of integers 0 ≤ r ≤ g such that g ≥ 3 or r > 0, there exists a (hyper)elliptic curve C over F2 of genus g and 2-rank r whose automorphism group consists of only identity and the (hyper)elliptic involution. As an application, we prove the existence of principally polarized abelian varieties (A, λ) over F2 of dimension g and 2-rank r such that Aut(A, λ) = {±1}.
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This paper examines the relationship between the automorphism group of a hyperelliptic curve defined over an algebraically closed field of characteristic two and the 2-rank of the curve. In particular, we exploit the wild ramification to use the Deuring-Shafarevich formula in order to analyze the ramification of hyperelliptic curves that admit extra automorphisms and use this data to impose res...
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Let α be an automorphism of a hyperelliptic curve C of genus g and let α be the automorphism induced by α on the genus-0 quotient of C by the hyperelliptic involution. Let n be the order of α and let n be the order of α. We show that the characteristic polynomial f of the automorphism α∗ of the Jacobian of C is determined by the values of n, n, and g, unless n = n, n is even, and (2g + 2)/n is ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2005
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-05-08294-8