Explicit arithmetic intersection theory and computation of N\'eron-Tate heights

Explicit arithmetic intersection theory and computation of N\'eron-Tate heights

We describe a general algorithm for computing intersection pairings on arithmetic surfaces. We have implemented our algorithm for curves over \mathbb{Q}, and we show how to use it to compute regulators for a number of Jacobians of smooth plane quartics, and to numerically verify the conjecture of Bi...

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Veröffentlicht in:Mathematics of computation 2020-01, Vol.89 (321), p.395
Hauptverfasser: Raymond van Bommel, David Holmes, J. Steffen Müller
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container_title Mathematics of computation
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creator Raymond van Bommel
David Holmes
J. Steffen Müller
description We describe a general algorithm for computing intersection pairings on arithmetic surfaces. We have implemented our algorithm for curves over \mathbb{Q}, and we show how to use it to compute regulators for a number of Jacobians of smooth plane quartics, and to numerically verify the conjecture of Birch and Swinnerton-Dyer for the Jacobian of the split Cartan curve of level 13, up to squares.
doi_str_mv 10.1090/mcom/3441
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title Explicit arithmetic intersection theory and computation of N\'eron-Tate heights
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