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Parallel weight 2 points on Hilbert modular eigenvarieties and the parity conjecture

Abstract:

Let F be a totally real field and let p be an odd prime which is totally split in F. We define and study one-dimensional ‘partial’ eigenvarieties interpolating Hilbert modular forms over F with weight varying only at a single place v above p. For these eigenvarieties, we show that methods developed by Liu, Wan and Xiao apply and deduce that, over a boundary annulus in weight space of sufficiently small radius, the partial eigenvarieties decompose as a disjoint union of components which are fi...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1017/fms.2019.23

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
Merton College
Role:
Author
ORCID:
0000-0002-9332-5204
More by this author
Role:
Author
ORCID:
0000-0003-4466-9518
Publisher:
Cambridge University Press Publisher's website
Journal:
Forum of Mathematics, Sigma Journal website
Volume:
7
Article number:
e27
Publication date:
2019-09-04
Acceptance date:
2019-06-17
DOI:
EISSN:
2050-5094
Language:
English
Keywords:
Pubs id:
1193797
Local pid:
pubs:1193797
Deposit date:
2021-09-03

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