On norm relations for Asai-Flach classes

2018/10/04 by Grossi, Giada · 2 citations
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1810.02273

Abstract

We give a new proof of the norm relations for the Asai-Flach Euler system built by Lei-Loeffler-Zerbes. More precisely, we redefine Asai-Flach classes in the language used by Loeffler-Skinner-Zerbes for Lemma-Eisenstein classes and prove both the vertical and the tame norm relations using local zeta integrals. These Euler system norm relations for the Asai representation attached to a Hilbert modular form over a quadratic real field F have been already proved by Lei-Loeffler-Zerbes for primes which are inert in F and for split primes satisfying some assumption; with this technique we are able to remove it and prove tame norm relations for all inert and split primes.

Cited by

• Euler systems for GSp(4) over imaginary quadratic fields
• The Asai--Flach Euler system in p-adic families

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