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Compatibility of arithmetic and algebraic local constants, II: the tame abelian potentially Barsotti–Tate case
Author(s) -
Nekovář Jan
Publication year - 2018
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms.12085
Subject(s) - mathematics , abelian group , galois module , abelian extension , modular form , arithmetic of abelian varieties , compatibility (geochemistry) , conjecture , elliptic curve , pure mathematics , iwasawa theory , complex multiplication , algebraic number , arithmetic , discrete mathematics , algebra over a field , elementary abelian group , rank of an abelian group , mathematical analysis , geochemistry , geology
We prove the compatibility of arithmetic local constants of Mazur and Rubin with the usual local constants for pairs of congruent self‐dual Galois representations that become Barsotti–Tate over a tamely ramified abelian extension. This allows us to complete the proof of the p ‐parity conjecture ( p > 2 ) for Selmer groups of Hilbert modular forms of parallel weight 2 and abelian varieties with real multiplication (in particular, elliptic curves) over totally real number fields.