l-adic algebraic monodromy groups, cocharacters, and the Mumford-Tate conjecture -- Web of Science v4.31

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l-adic algebraic monodromy groups, cocharacters, and the Mumford-Tate conjecture
Pink R
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK 495: 187-237 FEB 20 1998

Document type: Article

Language: English

Cited References: 47

Times Cited: 4

Abstract:
We prove that the l-adic algebraic monodromy groups associated to a motive over a number field are generated by certain one-parameter subgroups determined by Hedge numbers. In the special case of an abelian variety we obtain stronger statements saying roughly that the l-adic algebraic monodromy groups look like a Mumford-Tate group of some (other?) abelian variety. When the endomorphism ring is Z and the dimension satisfies certain numerical conditions, we deduce the Mumford-Tate conjecture for this abelian variety. We also discuss the problem of finding places of ordinary reduction.

KeyWords Plus:
ABELIAN-VARIETIES, L-INDEPENDENCE, REPRESENTATIONS, SYSTEMS, FIELDS

Addresses:
Pink R, Univ Mannheim, Fak Math & Informat, D-68131 Mannheim, Germany
Univ Mannheim, Fak Math & Informat, D-68131 Mannheim, Germany

Publisher:
WALTER DE GRUYTER & CO, BERLIN

IDS Number:
ZA930

ISSN:
0075-4102

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