Coleman–Gross height pairings and the p-adic sigma function
نویسندگان
چکیده
منابع مشابه
Height pairings on Shimura curves and p-adic uniformization
In a recent paper [16] of one of us it was shown that there is a close connection between the value of the height pairing of certain arithmetic 0-cycles on Shimura curves and the values at the center of their symmetry of the derivatives of certain metaplectic Eisenstein series of genus 2. On the one hand, the height pairing can be written as a sum of local height pairings. For example, if the 0...
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We give a formula for the component at p of the p-adic height pairing of a divisor of degree 0 on a hyperelliptic curve. We use this to give a Chabauty-like method for finding p-adic approximations to p-integral points on such curves when the Mordell-Weil rank of the Jacobian equals the genus. In this case we get an explicit bound for the number of such p-integral points, and we are able to use...
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In [CG89], Coleman and Gross proposed a definition of a p-adic height pairing on curves over number fields with good reduction at primes above p. The pairing was defined as a sum of local terms and the most interesting terms are the ones corresponding to primes above p where the definition depends on Coleman’s theory of p-adic integration. Later, Nekovář constructed in [Nek93] a general p-adic ...
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It is noted that an efficient algorithm for calculating a p-adic height could have cryptanalytic applications. Elliptic curves and their generalizations are an active research topic with practical applications in cryptography [1], [2], [3]. If E is an elliptic curve defined over a finite field Fp, where p is prime, and if P and Q are points on the curve E such that Q = nP , then the elliptic cu...
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We prove that for abelian varieties with semistable ordinary reduction the p-adic Mazur-Tate height pairing is induced by the unit root splitting of the Hodge filtration on the first deRham cohomology.
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ژورنال
عنوان ژورنال: Journal für die reine und angewandte Mathematik (Crelles Journal)
سال: 2015
ISSN: 0075-4102,1435-5345
DOI: 10.1515/crelle-2012-0095