Mathematische Annalen

, Volume 370, Issue 3–4, pp 1079–1175 | Cite as

Regular formal moduli spaces and arithmetic transfer conjectures

  • M. Rapoport
  • B. SmithlingEmail author
  • W. Zhang


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 work. We prove these conjectures in low-dimensional cases.



We are grateful to U. Görtz, X. He, and S. Yu for helpful discussions. We also acknowledge the hospitality of the ESI (Vienna) and the MFO (Oberwolfach), where part of this work was carried out. We finally thank the referee for his/her remarks on the text. M.R. is supported by a Grant from the Deutsche Forschungsgemeinschaft through the Grant SFB/TR 45. B.S. is supported by a Simons Foundation Grant #359425 and an NSA Grant H98230-16-1-0024. W.Z. is supported by NSF Grants DMS #1301848 and #1601144, and by a Sloan research fellowship.


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© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Mathematisches Institut der Universität BonnBonnGermany
  2. 2.Department of MathematicsJohns Hopkins UniversityBaltimoreUSA
  3. 3.Department of MathematicsColumbia UniversityNew YorkUSA

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