Given an arithmetic variety $f: X \rightarrow Spec(\mathbb{Z})$.

Is there a notion of boundedness for families of sheaves on $X$?

I only found the notion for families on the fibers of $f$. But i am interested in sheaves defined on $X$.

All definitions / theorems i found only work when $X$ is defined over some field $k$, where one has the Hilbert polynomial, slope etc, which we don't have in this case. Is there some substitute for these terms?

Or are there even results about moduli spaces of sheaves on arithmetic varieties?

Given an arithmetic variety $f: X \rightarrow Spec(\mathbb{Z})$.

Is there a notion of boundedness for families of sheaves on $X$?

I only found the notion for families on the fibers of $f$. But i am interested in sheaves defined on $X$.

All definitions / theorems i found only work when $X$ is defined over some field $k$, where one has the Hilbert polynomial, slope etc, which we don't have in this case. Is there some substitute for these terms?

Or are there even results about moduli spaces of sheaves on arithmetic varieties?

Edit: According to http://arxiv.org/abs/math/0612268 there is a notion of arithmetic (semi)stability. One even has a Harder Narasimhan filtration. Can one define the notion of boundedness in the Arakelov setting? Are there any results on moduli spaces of vector bundles in Arakelov theory?