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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 $\bar{X}$ ...

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 ...