Modular Heights of Unitary Shimura Varieties III: Proof of the Main Theorem

@misc{guo2026modular,
  title = {{Modular Heights of Unitary Shimura Varieties III: Proof of the Main Theorem}},
  author = {Ziqi Guo},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2606.19158},
  eprint = {2606.19158},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.19158},
}

TY  - UNPB
TI  - Modular Heights of Unitary Shimura Varieties III: Proof of the Main Theorem
AU  - Ziqi Guo
PY  - 2026
DA  - 2026/10/09
PB  - arXiv
DO  - 10.48550/arxiv.2606.19158
UR  - https://arxiv.org/abs/2606.19158
AB  - This is the third and the last of a series of three papers, in which we prove a formula expressing the modular height of a unitary Shimura variety over a CM number field in terms of the logarithmic derivative of the Hecke L-function associated with the CM extension. The main idea of our proof is to compare the holomorphic projection of the derivative of a certain mixed Eisenstein-theta series and the arithmetic degree of a generating series of divisors on unitary Shimura varieties. In this paper, we compute the arithmetic degree of the arithmetic generating series of divisors on unitary Shimura varieties, and then, combining with the results from the first two papers in this series, derive the modular height formula for unitary Shimura varieties.
ER  -