Unitary cycles on Shimura curves and the Shimura lift I

Siddarth Sankaran

Unitary cycles on Shimura curves and the Shimura lift I

Number Theory 2014-05-15 v2 Algebraic Geometry

Authors: Siddarth Sankaran

Abstract

This paper concerns two families of divisors, which we call the `orthogonal' and `unitary' special cycles, defined on integral models of Shimura curves. The orthogonal family was studied extensively by Kudla-Rapoport-Yang, who showed that they are closely related to the Fourier coefficients of modular forms of weight 3/2, while the `unitary' divisors are analogues of cycles appearing in more recent work of Kudla-Rapoport on unitary Shimura varieties. Our main result shows that these two families are related by (a formal version of) the Shimura lift.

Keywords

shimura curves special cycles shimura lift integral models modular forms kudla-rapoport-yang

Cite

@article{arxiv.1302.4650,
  title  = {Unitary cycles on Shimura curves and the Shimura lift I},
  author = {Siddarth Sankaran},
  journal= {arXiv preprint arXiv:1302.4650},
  year   = {2014}
}

Comments

62 pages. Some material from arXiv:1309.2083v1 has been incorporated here, and the main result has been strengthened. Also minor changes to exposition and organization

Unitary cycles on Shimura curves and the Shimura lift I

Abstract

Keywords

Cite

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