Regular formal moduli spaces and arithmetic transfer conjectures

2016/04/08 by Michael Rapoport, Rapoport, Michael, Brian D. Smithling +3 · 2 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1604.02419

openalex publication_date 2016/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define various formal moduli spaces of p-divisible groups which are regular, and morphisms between them. We formulate arithmetic transfer conjectures, which are variants of the arithmetic fundamental lemma conjecture of the third author in the presence of ramification. These conjectures include the AT conjecture of our previous joint paper. We prove these conjectures in low-dimensional cases.

Citations

• Basic loci in Shimura varieties of Coxeter type
• The supersingular locus of unitary Shimura varieties with exotic good reduction

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

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