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A proof of a conjecture of Y. Morita
Author(s) -
Lee Dong Uk
Publication year - 2012
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdr104
Subject(s) - mathematics , conjecture , abelian group , morita therapy , pure mathematics , unipotent , generalization , group (periodic table) , reduction (mathematics) , abelian variety , discrete mathematics , combinatorics , mathematical analysis , geometry , chemistry , organic chemistry
A conjecture of Morita says that if an abelian variety defined over a number field has the Mumford–Tate group which does not have any non‐trivial ℚ‐rational unipotent element, then it has potentially good reduction everywhere. In this article, we prove this conjecture. The main ingredients of the proof include some newly established cases of the conjecture due to Vasiu, a generalization of a criterion of Paugam on good reduction of abelian varieties, and the local–global principle of isotropy for Mumford–Tate groups of abelian varieties.