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Explicit Coleman integration for curves
Mathematics of Computation ( IF 2 ) Pub Date : 2020-05-22 , DOI: 10.1090/mcom/3542
Jennifer Balakrishnan , Jan Tuitman

The Coleman integral is a $p$-adic line integral that plays a key role in computing several important invariants in arithmetic geometry. We give an algorithm for explicit Coleman integration on curves, using the algorithms of the second author to compute the action of Frobenius on $p$-adic cohomology. We present a collection of examples computed with our implementation. This includes integrals on a genus 55 curve, where other methods do not currently seem practical.

中文翻译:

曲线的显式 Coleman 积分

Coleman 积分是一个 $p$-adic 线积分,它在计算算术几何中的几个重要不变量中起着关键作用。我们给出了曲线上显式 Coleman 积分的算法,使用第二作者的算法来计算 Frobenius 对 $p$-adic 上同调的作用。我们提供了一组使用我们的实现计算的示例。这包括在属 55 曲线上的积分,其他方法目前似乎不实用。
更新日期:2020-05-22
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