Explicit Coleman integration in larger characteristic
نویسندگان
چکیده
منابع مشابه
Explicit Coleman Integration for Hyperelliptic Curves
Coleman’s theory of p-adic integration figures prominently in several number-theoretic applications, such as finding torsion and rational points on curves, and computing p-adic regulators in K-theory (including p-adic heights on elliptic curves). We describe an algorithm for computing Coleman integrals on hyperelliptic curves, and its implementation in Sage.
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We show that the linear dependence on p of the running time of Kedlaya’s point-counting algorithm in characteristic p can be reduced to p1/2, at least in the simplest case of an elliptic curve over the prime field.
متن کاملHeidelberg lectures on Coleman integration
In the first half of February 2010 I spent 2 weeks at the Mathematics Center Heidelberg (MATCH) at the university of Heidelberg, as part of the activity PIA 2010 The arithmetic of fundamental groups. In the first week I gave 3 introductory lectures on Coleman integration theory and in the second week I gave a research lecture on new work, which was (and still is) in progress, concerning Coleman...
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The theory of Coleman integration has been developed in a number of directions by Coleman [Col82, Col85, CdS88] and later by the author [Bes00a] (a totally different approach was worked out by Colmez [Col98] and by Zarhin [Zar96]). It provides a way of extending the ring of analytic functions on certain rigid analytic domains in such a way that one can often find an essentially unique primitive...
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As part of my introductory lectures on Coleman integration, to be published in the proceedings of PIA 2010 The arithmetic of fundamental groups, I discussed the Galois theory of differential equations and the theory of differential Tannakian categories, with a speculative application to Coleman integration in families. The referee of the paper thought it was not appropriate to discuss this mate...
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ژورنال
عنوان ژورنال: The Open Book Series
سال: 2019
ISSN: 2329-907X,2329-9061
DOI: 10.2140/obs.2019.2.85