Euler systems for Hilbert modular surfaces

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.

arXiv commentFinal version, to appear in "Forum of Mathematics, Sigma"

References in corpus (15)

• Rankin--Eisenstein classes and explicit reciprocity laws
• Euler systems for Rankin--Selberg convolutions of modular forms
• Rankin--Eisenstein classes for modular forms
• Syntomic cohomology and regulators for varieties over p-adic fields
• On Ihara's lemma for Hilbert Modular Varieties
• Coleman maps and the p-adic regulator
• Images of adelic Galois representations for modular forms
• p-adic Cohomology and classicality of overconvergent Hilbert modular forms
• Decomposition de motifs abeliens
• Euler systems for modular forms over imaginary quadratic fields
• On the interior motive of certain Shimura varieties: the case of Hilbert-Blumenthal varieties
• Hirzebruch-Zagier cycles and twisted triple product Selmer groups
• Syntomic regulators of Asai--Flach classes
• Regulators for Rankin-Selberg products of modular forms
• Non-paritious Hilbert modular forms

Cited by in corpus (15)

• Higher Hida theory and p-adic L-functions for GSp(4)
• Spherical varieties and norm relations in Iwasawa theory
• Syntomic regulators of Asai--Flach classes
• P-adic Asai L-functions of Bianchi modular forms
• Gross--Prasad periods for reducible representations
• Triple product p-adic L-functions for Shimura curves over totally real number fields
• Non-paritious Hilbert modular forms
• On integral aspects of Asai periods and Euler systems for ${\mathrm{Res}}_{E/\mathbf{Q}}{\mathrm{GL}}_2$
• Tempered currents and Deligne cohomology of Shimura varieties, with an application to ${\mathrm{GSp}}_6$
• Poles of p-adic Asai L-functions and distinguished representations
• Control Theorems for Hilbert Modular Varieties
• On the factorisation of the $p$-adic Rankin-Selberg $L$-function in the supersingular case
• Finite slope Triple Product p-adic L-functions over totally real fields
• Higher Hida theory for Hilbert modular varieties in the totally split case
• Norm-compatible systems of cohomology classes for $\mathrm{GU}(2,2)$