15 citations · 48 across the 15 of their papers we have counts for
14 papers · 1 filter
The convergence Newton polygon of a -adic differential equation IV : controlling graphs
Jérôme Poineau, Andrea Pulita
In our previous works we proved a finiteness property of the radii of convergence functions associated with a vector bundle with connection on -adic analytic curves. We showed t…
Regular singular differential modules over differential rings
Andrea Pulita
We obtain Fuchs decomposition theorem for regular singular differential modules over a large class of differential rings. We provide a definition of regularity inspired by differen…
Solvability of rank one -adic differential and -difference equations over the Amice ring
Andrea Pulita
We provide a necessary and sufficient condition for the solvability of a rank one differential (resp. -difference) equation over the Amice's ring. We also extend to that ring a…
Small Connections are cyclic
Andrea Pulita
The main local invariants of a (one variable) differential module over the complex numbers are given by means of a cyclic basis. In the -adic setting the existence of a cyclic v…
The convergence Newton polygon of a -adic differential equation V : local index theorems
Jérôme Poineau, Andrea Pulita
In this paper and its sequel we consider locally-free -modules together with a connection over a quasi-smooth Berkovich curve . We obtain necessary and sufficient…
The convergence Newton polygon of a -adic differential equation III : global decompositions
Jérôme Poineau, Andrea Pulita
We deal with locally free -modules with connection over a Berkovich curve . As a main result we prove local and global decomposition theorems of such objects by t…