## Duke Mathematical Journal

- Duke Math. J.
- Volume 166, Number 12 (2017), 2183-2336.

### On the arithmetic transfer conjecture for exotic smooth formal moduli spaces

M. Rapoport, B. Smithling, and W. Zhang

#### Abstract

In the relative trace formula approach to the arithmetic Gan–Gross–Prasad conjecture, we formulate a local conjecture (arithmetic transfer) in the case of an exotic smooth formal moduli space of $p$-divisible groups, associated to a unitary group relative to a ramified quadratic extension of a $p$-adic field. We prove our conjecture in the case of a unitary group in three variables.

#### Article information

**Source**

Duke Math. J. Volume 166, Number 12 (2017), 2183-2336.

**Dates**

Received: 31 March 2015

Revised: 3 November 2016

First available in Project Euclid: 9 June 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.dmj/1496995226

**Digital Object Identifier**

doi:10.1215/00127094-2017-0003

**Subjects**

Primary: 11G18: Arithmetic aspects of modular and Shimura varieties [See also 14G35]

Secondary: 14G17: Positive characteristic ground fields 22E50: Representations of Lie and linear algebraic groups over local fields [See also 20G05]

**Keywords**

arithmetic Gan–Gross–Prasad conjecture arithmetic fundamental lemma Rapoport–Zink space special cycles

#### Citation

Rapoport, M.; Smithling, B.; Zhang, W. On the arithmetic transfer conjecture for exotic smooth formal moduli spaces. Duke Math. J. 166 (2017), no. 12, 2183--2336. doi:10.1215/00127094-2017-0003. https://projecteuclid.org/euclid.dmj/1496995226.