Abstract
We prove a variant of the arithmetic fundamental lemma conjecture of Wei Zhang for n = 2. More precisely, we consider the deformation lengths of certain quasi-homomorphisms of quasi-canonical lifts in the sense of Gross. We prove the existence of a test function on a symmetric space related to GL 2 whose orbital integrals over GL 1 equal the deformation lengths in question.
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References
ARGOS Seminar in Bonn: Intersections of Modular Correspondences, Astérisque vol. 312 (2007)
Gross B.: On canonical and quasi-canonical liftings. Invent. Math. 84, 321–326 (1986)
Gross B., Keating K.: On the intersection of modular correspondences. Invent. Math. 112, 225–245 (1993)
Keating K.: Lifting endomorphisms of formal A-modules. Compos. Math. 67, 211–239 (1988)
Kudla S., Rapoport M.: Special cycles on unitary Shimura varieties I, unramified local theory. Invent. Math. 184, 629–682 (2011)
Rapoport, M.: Deformations of isogenies of of formal groups, in [1], pp. 139–169
Rapoport, M., Smithling, B., Zhang, W.: On the Arithmetic Transfer Conjecture for Exotic Smooth Formal Moduli Spaces, preprint, arXiv:1503.06520 (2015)
Rapoport, M., Smithling, B., Zhang, W.: On Arithmetic Transfer: Conjectures (in preparation)
Rapoport M., Terstiege U., Zhang W.: On the arithmetic fundamental lemma in the minuscule case. Compos. Math. 149, 1631–1666 (2013)
Viehmann, E., Ziegler, K.: Formal Moduli of Formal \({\mathcal{O}_K}\)-modules, in [1], pp. 57–66
Vollaard, I.: Endomorphisms of Quasi-canonical Lifts, in [1], pp. 105–112
Wewers, S.: Canonical and Quasi-canonical Liftings, in [1], pp. 67–86
Zhang W.: On arithmetic fundamental lemmas. Invent. Math. 188, 197–252 (2012)
Zhang W.: On the smooth transfer conjecture of Jacquet–Rallis for n = 3. Ramanujan J. 29, 225–256 (2012)
Zhang W.: Fourier transform and the global Gan–Gross–Prasad conjecture for unitary groups. Ann. Math. 180, 971–1049 (2014)
