3 problems

Goncharov's regulator image conjecture. The image of this regulator map in Deligne cohomology coincides with the image of Beilinson's regulator map.

Beilinson's conjecture. The composition

Beilinson's conjecture. With notation as above, if a class in $CH^n(X)_{\mathbb Q}$ vanishes in $H^i\left(k,H^{2n-i}(X_{\bar k},\mathbb Q_\ell(n))\right)$ for $i=0,1$, then it does…