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Results tagged with motives
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user 350762
for questions about motives in algebraic geometry, including constructions of categories of motives and motivic sheaves, and aspects of the standard conjectures.
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Motives based on Hodge cycles vs algebraic cycles
I am not a specialist of motives. I am afraid my questions are rather naive.
We have the category of (pure) motives based on Hodge cycles by Deligne. … In his articles with Milne, morphisms between motives are defined using absolute Hodge cycles.
On the the hand we have the (triangulated) category of (mixed) motives based on Voevodsky. …
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3
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answer
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Elementary questions on motives
I have the following questions on them.
①Do we have a proof that abelian varieties and tori are motives? Do we have a theory on the category of objects consisting of motives and algebraic varieties? … ③Motives are direct factors of cohomology, but I do not find any definition of motives using cohomology. I know their definition using hodge cycles and algebraic cycles. …
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Roots of weight of a characteristic polynomial of Frobenius
Edit:motives are defined by numerical equivalence of algebraic cycles, good reduction of motives are defined by the corresponding l-adic representation is unramified …
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