Year: 2026
Type: preprint
Abstract: We prove that for any prime $p$ and tame level $N$, the weight map from the cuspidal Hilbert eigenvariety constructed by Andreatta-Iovita-Pilloni for a totally real field $F$ to the weight space is proper in the sense of Buzzard-Calegari, under a non-vanishing hypothesis on certain Sen polynomials of Galois representations at the primes above $p$. In particular, this yields the properness of the eigenvariety away from non-positive integral Sen weights. Our approach extends the $p$-adic Hodge-theoretic argument of Diao-Liu.
Source: arXiv (Cornell University)
Author: Zhu, Yi
Institution: Tsinghua University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221537581