Geodesic
Modularity of arithmetic special divisors for unitary Shimura varieties (with an appendix by Yujie Xu)
Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e111

Voir la notice de l'article provenant de la source Cambridge University Press

We construct explicit generating series of arithmetic extensions of Kudla’s special divisors on integral models of unitary Shimura varieties over CM fields with arbitrary split levels and prove that they are modular forms valued in the arithmetic Chow groups. This provides a partial solution to Kudla’s modularity problem. The main ingredient in our construction is S. Zhang’s theory of admissible arithmetic divisors. The main ingredient in the proof is an arithmetic mixed Siegel-Weil formula. 
Qiu, Congling; Xu, Yujie. Modularity of arithmetic special divisors for unitary Shimura varieties (with an appendix by Yujie Xu). Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e111. doi: 10.1017/S2050509425000003
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