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ALGEBRAIC TORI AS DEGENERATIONS OF ABELIAN VARIETIES
Author(s) -
Lan KaiWen,
Suh Junecue
Publication year - 2018
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579317000420
Subject(s) - mathematics , abelian group , arithmetic of abelian varieties , abelian variety , torus , abelian variety of cm type , endomorphism , algebraic number , scheme (mathematics) , pure mathematics , rank of an abelian group , elementary abelian group , fiber , algebra over a field , mathematical analysis , geometry , chemistry , organic chemistry
We first show that every algebraic torus over any field, not necessarily split, can be realized as the special fiber of a semi‐abelian scheme whose generic fiber is an absolutely simple abelian variety. Then we investigate which algebraic tori can be thus obtained, when we require the generic fiber of the semi‐abelian scheme to carry non‐trivial endomorphism structures.