Finiteness for crystalline representations of the absolute Galois group of a totally real field

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Let K be a totally real field and G(K) := Gal((K) over bar /K) its absolute Galois group, where K is a fixed algebraic closure of (K) over bar. Let e be a prime and E a finite extension of Q(l). Let S be a finite set of finite places of K not dividing l. Assume that K, S, Hodge-Tate type h and a positive integer n are fixed. In this paper, we prove that if 2 is sufficiently large, then, for any fixed E, there are only finitely many isomorphism classes of crystalline representations r : G(K) -> GL(n)(E) unramified outside S boolean OR {v : v vertical bar l}, with fixed Hodge-Tate type h, such that r vertical bar G(K') similar or equal to circle plus r(i)' for some finite totally real field extension K' of K unramified at all places of K over l, where each representation r(i)'over E is an 1-dimensional representation of G(K)' or a totally odd irreducible 2-dimensional representation of G(K)' with distinct Hodge-Tate numbers.
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Issue Date
2020-04
Language
English
Article Type
Article
Citation

JOURNAL OF NUMBER THEORY, v.209, pp.312 - 329

ISSN
0022-314X
DOI
10.1016/j.jnt.2019.08.023
URI
http://hdl.handle.net/10203/272351
Appears in Collection
MA-Journal Papers(저널논문)
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