English

The Kudla-Rapoport conjecture at a ramified prime for $U(1, 1)$

Number Theory 2023-06-26 v3

Abstract

In this paper, we proved a local arithmetic Siegel-Weil formula for a U(1,1)U(1, 1)-Shimura variety at a ramified prime, a.k.a. a Kudla-Rapoport conjecture at a ramified case. The formula needs to be modified from the original Kudla-Rapoport conjecture. In the process, we also gives an explicit decomposition of the special divisors of the Rapoport-Zink space of unitary type (1,1)(1, 1) (Kr\"amer model). A key ingredient is to relate the Rapoport-Zink space to the Drinfeld upper plane.

Keywords

Cite

@article{arxiv.2011.01356,
  title  = {The Kudla-Rapoport conjecture at a ramified prime for $U(1, 1)$},
  author = {Qiao He and Yousheng Shi and Tonghai Yang},
  journal= {arXiv preprint arXiv:2011.01356},
  year   = {2023}
}

Comments

34pp, final version, published in Transactions of the AMS