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Albanese Standard and Albanese Exotic Varieties
Author(s) -
Schoen Chad
Publication year - 2006
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610706023076
Subject(s) - mathematics , abelian group , algebraically closed field , pure mathematics , conjecture , variety (cybernetics) , class (philosophy) , abelian variety , algebraic number , field (mathematics) , arithmetic of abelian varieties , mathematical analysis , elementary abelian group , computer science , rank of an abelian group , statistics , artificial intelligence
Smooth complete algebraic varieties defined over an algebraically closed field are divided into two classes according to the behaviour of the albanese map. Criteria are given for when a variety belongs to either class. The relationship with the Tate conjecture for abelian varieties is discussed.