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Hensel-lifting torsion points on Jacobians, and Galois representations from higher étale cohomology spaces

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No logo availableTechnische Universität Braunschweig
 Mascot, Nicolas

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Hensel-lifting torsion points on Jacobians, and Galois representations from higher étale cohomology spaces
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31
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CC Attribution 3.0 Germany:
You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
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Abstract
We describe an algorithm to p-adically lift torsion points on Jacobians of curves. As an application, we show how to compute explicitly mod l Galois representations occurring in the Jacobians of curves, and also more generally in higher étale cohomology spaces of higher-dimensional varieties. This has many applications, ranging from exploring Langlands's program to point counting in cryptography.