The unramified Witt group of hyperelliptic curves in characteristic 2
نویسندگان
چکیده
منابع مشابه
Hyperelliptic Curves in Characteristic 2
In this paper we prove that there are no hyperelliptic supersingular curves of genus 2n − 1 in characteristic 2 for any integer n ≥ 2. Let F be an algebraically closed field of characteristic 2, and let g be a positive integer. Write h = blog2(g + 1) + 1c, where b c denotes the greatest integer less than or equal to a given real number. Let X be a hyperelliptic curve over F of genus g ≥ 3 of 2-...
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Let ĒΓ be a family of hyperelliptic curves over F cl 2 with general Weierstrass equation given over a very small field F. We describe in this paper an algorithm for computing the zeta function of Ēγ̄, with γ̄ in a degree n extension field of F, which has as time complexity Õ(n3) bit operations and memory requirements O(n2) bits. With a slightly different algorithm we can get time O(n2.667) and me...
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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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In a letter to Dirichlet, dated May 30, 1828 ([5]), Gauß considered the divisibility of the class number of Q( √−p) (p prime, = 1 mod 4) by 8. Many variations on this theme can be found in the mathematical literature of the subsequent centuries, either using quadratic forms or class field theory ( Rédei [15], Barrucand-Cohn [3], Hasse [10], Kaplan [12], Stevenhagen [17]). Of these, the latter a...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2008
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2007.11.002