All Questions

Can sheaf cohomology on the Zariski-Riemann spaces give some sort of classification for field extensions (even just for function fields)? If not, are there any significant or useful results (e.g. for ...

I'm studying Proposition 6.2.3 from Goss "Basic Structures of Function Field Arithmetic", page 184: Let $F$ be the sheaf of Data A (a torsion-free coherent $O_{\bar{X}}$-module on $\bar{X}$ ...