Timeline for Sheaf of power-bounded elements in rigid analytic geometry
Current License: CC BY-SA 2.5
2 events
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| Dec 11, 2010 at 18:15 | comment | added | BCnrd | Dear Joel: The sheaf property doesn't seem to need a reference (it's obvious, as you say). For disc.-valued $k$, if $\mathfrak{X}$ is a normal flat top. lft formal scheme over $O_k$ and $X = \mathfrak{X}^{\rm{rig}}$ then ring of global fns on $\mathfrak{X}$ maps isomorphically onto ring of power-bounded fns on $X$ (see Thm. 7.4.1 deJong's IHES paper "Crystalline Dieudonne theory..."). Also, by 6.4.1/6 in BGR, $A^0$ is top. f.type over $O_k$ for any $k$-affinoid $A$ in discr.-valued case, but formation is bad for surjections (see BGR, 6.4.3), so a "useful" Kiehl-type theory seems unlikely. | |
| Dec 11, 2010 at 17:23 | history | asked | Joël | CC BY-SA 2.5 |