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arXiv · 1607.07813

Euler systems for Hilbert modular surfaces

Antonio Lei·David Loeffler·Sarah Livia Zerbes
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Abstract

We construct an Euler system -- a compatible family of global cohomology classes -- for the Galois representations appearing in the geometry of Hilbert modular surfaces. If a conjecture of Bloch and Kato on injectivity of regulator maps holds, this Euler system is non-trivial, and we deduce bounds towards the Iwasawa main conjecture for these Galois representations.

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Antonio Lei, David Loeffler, Sarah Livia Zerbes. 2016-07-26. Euler systems for Hilbert modular surfaces. https://doi.org/10.1017/fms.2018.23

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