Geodesic
A $p$-adic local monodromy theorem
Kiran S. Kedlaya1
1Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, United States
Annals of mathematics, Tome 160 (2004) no. 1, pp. 93-184
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We produce a canonical filtration for locally free sheaves on an open $p$-adic annulus equipped with a Frobenius structure. Using this filtration, we deduce a conjecture of Crew on $p$-adic differential equations, analogous to Grothendieck’s local monodromy theorem (also a consequence of results of André and of Mebkhout). Namely, given a finite locally free sheaf on an open $p$-adic annulus with a connection and a compatible Frobenius structure, the module admits a basis over a finite cover of the annulus on which the connection acts via a nilpotent matrix.

DOI : 10.4007/annals.2004.160.93

Kiran S. Kedlaya  1

1 Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, United States 
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Kiran S. Kedlaya. A $p$-adic local monodromy theorem. Annals of mathematics, Tome 160 (2004) no. 1, pp. 93-184. doi: 10.4007/annals.2004.160.93

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