Abstract: Let p be an odd prime number and be a p-adic analytic family of potentially semi-stable representations with an arithmetic progression Under some assumptions, we shall prove in this article that if there exists some such that the -representation associated to is reducible, then for any is also reducible, where is the Weil group of the field of p-adic numbers.
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Keywords and phrases: potentially semi-stable representations, Weil group.
Received: June 27, 2023; Accepted: August 1, 2023; Published: August 28, 2023
How to cite this article: Atsushi Yamagami, On some property of p-adic families of potentially semi-stable representations, JP Journal of Algebra, Number Theory and 62(1) (2023), 51-69. http://dx.doi.org/10.17654/0972555523021
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