Publications [#374141] of Jessica Fintzen

Papers Published

1. Caraiani, A; Eischen, E; Fintzen, J; Mantovan, E; Varma, I, p-Adic q-Expansion Principles on Unitary Shimura Varieties, in Association for Women in Mathematics Series, vol. 3 (January, 2016), pp. 197-243 [doi]
   (last updated on 2024/07/10)

   Abstract:
   We formulate and prove certain vanishing theorems for p-adic automorphic forms on unitary groups of arbitrary signature. The p-adic q-expansion principle for p-adic modular forms on the Igusa tower says that if the coefficients of (sufficiently many of) the q-expansions of a p-adic modular form f are zero, then f vanishes everywhere on the Igusa tower. There is no p-adic q-expansion principle for unitary groups of arbitrary signature in the literature. By replacing q-expansions with Serre–Tate expansions (expansions in terms of Serre–Tate deformation coordinates) and replacing modular forms with automorphic forms on unitary groups of arbitrary signature, we prove an analogue of the p-adic q-expansion principle. More precisely, we show that if the coefficients of (sufficiently many of) the Serre–Tate expansions of a p-adic automorphic form f on the Igusa tower (over a unitary Shimura variety) are zero, then f vanishes identically on the Igusa tower.This paper also contains a substantial expository component. In particular, the expository component serves as a complement to Hida’s extensive work on p-adic automorphic forms.