Constructs a new anticyclotomic Euler system for Asai Galois representations attached to p-ordinary Hilbert modular forms, with norm relations and p-adic interpolation.
An Euler system for the adjoint of a modular form
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abstract
We construct an Euler system for the adjoint Galois representation of a modular form, using motivic cohomology classes arising from Hilbert modular surfaces. We use this Euler system to give an upper bound for the Selmer group of the adjoint representation over the cyclotomic Zp-extension, which agrees with the predictions of the Iwasawa main conjecture up to powers of p.
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An anticyclotomic Euler system of Hirzebruch--Zagier cycles I: Norm relations and $p$-adic interpolation
Constructs a new anticyclotomic Euler system for Asai Galois representations attached to p-ordinary Hilbert modular forms, with norm relations and p-adic interpolation.