TITLE: Motivic $\mathbf{Z}(1)$
QUESTION [7 upvotes]: I know that the Bloch higher Chow complex, $\mathbf{Z}(i)_{\mathcal{M}}$, on a smooth scheme over a field $k$, reads, in degree $1$:
$$\mathbf{Z}(1)_{\mathcal{M}}\simeq\mathbf{G}_m[-1].$$
How to see this? I did not find it anywhere clearly stated and proved in the literature.
Is there a motivic exponential sequence of some kind? (not that I know) so as to say the complex $0\to \mathbf{Z}(1)\to\mathbf{G}_a\to 0$, which ought to be $\mathbf{Z}(1)_{\mathcal{M}}$, should be quasi-isomorphic to $\mathbf{G}_m[-1]$ via some exponential? (but what is $\mathbf{Z}(1)$, let alone the exponential?!) 
This is what happens for Deligne cohomology, for instance.

REPLY [2 votes]: This statement is proven in the article "The Bloch Complex in Codimension One and Arithmetic Duality". The proof is very elementary.
Also it can be found in the "Lecture Notes on Motivic Cohomology" by
Carlo Mazza,Vladimir Voevodsky and Charles Weibel, Part 1 lecture 4.