Relative unitary RZ-spaces and the Arithmetic Fundamental Lemma

2016/11/20 by Mihatsch, Andreas · 2 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1611.06520

Abstract

We verify new cases of the Arithmetic Fundamental Lemma (AFL) of Wei Zhang. This relies on a recursive algorithm which allows, under certain conditions, to reduce the AFL identity in question to an AFL identity in lower dimension. The main ingredient for this reduction is a comparison isomorphism between different moduli problems of PEL-type for p-divisible groups. The construction of this comparison isomorphism is based on the theory of relative displays and frames, as developed by Tobias Ahsendorf, Eike Lau and Thomas Zink.

Cited by

• The basic locus of regular ramified unitary Rapoport-Zink spaces at vertex-stabilizer level
• The basic locus of unitary splitting Rapoport-Zink spaces with vertex stabilizer level

Related

• Weil representation and Arithmetic Fundamental Lemma
• More Arithmetic Fundamental Lemma conjectures: the case of Bessel subgroups
• The Geometric Nature of the Fundamental Lemma
• On the Arithmetic Fundamental Lemma through Lie algebras
• On the Linear AFL: The Non-Basic Case