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Ampleness of Automorphic Line Bundles on $U(2)$ Shimura Varieties | | Deding Yang
; | | Date: |
1 Sep 2023 | | Abstract: | Let $F$ be a totally real field in which $p$ is unramfied and let $S$ denote
the integral model of the Hilbert modular variety with good reduction at $p$.
Consider the usual automorphic line bundle $mathcal{L}$ over $S$. On the
generic fiber, it is well known that $mathcal{L}$ is ample if and only if all
the coefficients are positive. On the special fiber, it is conjectured in
citep{Tian-Xiao} that $mathcal{L}$ is ample if and only if the coefficients
satisfy certain inequalities. We prove this conjecture for $U(2)$ Shimura
varieties in this paper and deduce a similar statement for Hilbert modular
varieties from this. | | Source: | arXiv, 2309.00286 | | Services: | Forum | Review | PDF | Favorites | |
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