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What is the relation between Beilinson's conjectures and Standard conjectures of algebraic cycles?

Do Standard conjectures on the K-theory of varieties over finite field have implications in the motivic cohomology of Z where exist the correct formalism of Beilinson's conjectures? What is the ...
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Absolute Hodge cycles over $\mathbf{Q}$

In the 1986 notes by Milne "Hodge cycles on abelian varieties", Deligne defines the notion of absolute Hodge cycles. For a smooth projective variety defined over $k\subset\mathbf{C}$ non ...
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Should all cohomology theories have a smooth proper base change

Let $H$ be a cohomology theory with respect to some Grothendieck topology (e.g. Zariski, analytic, etale, fppf, Nisnevich, etc.) Does H satisfy smooth proper base? If yes, does this mean that "...
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