LOG-GROWTH FILTRATION AND FROBENIUS SLOPE FILTRATION OF F-ISOCRYSTALS AT THE GENERIC AND SPECIAL POINTS

作者：Chiarellotto Bruno^*; Tsuzuki Nobuo

来源：Documenta Mathematica, 2011, 16: 33-69.

DOI：10.4171/dm/326

• p-adic differential equations
• logarithmic growth
• Frobenius slopes
• Newton polygon

We study, locally on a curve of characteristic p > 0, the relation between the log-growth filtration and the Frobenius slope filtration for F-isocrystals, which we will indicate as phi-del-modules, both at the generic point and at the special point. We prove that a bounded phi-del-module at the generic point is a direct sum of pure phi- del-modules. By this splitting of Frobenius slope filtration for bounded modules we will introduce a filtration for phi-del-modules (PBQ filtration). We solve our conjectures of comparison of the log-growth filtration and the Frobenius slope filtration at the special point for particular phi-del-modules (HPBQ modules). Moreover we prove the analogous comparison conjecture for PBQ modules at the generic point. These comparison conjectures were stated in our previous work [CT09]. Using PBQ filtrations for phi-del-modules, we conclude that our conjecture of comparison of the log-growth filtration and the Frobenius slope filtration at the special point implies Dwork's conjecture, that is, the special log-growth polygon is above the generic log-growth polygon including the coincidence of both end points.

• 出版日期2011