References: p-adic Differential Equations by Kiran S. Kedlaya
The radius of convergence of local horizontal sections is an important but coarse numerical invariant of differential modules, we need to control it to produce solutions of \(p\)-adic differential equations.
It is often difficult to compute, but an interesting idea of Dwork is that we can have good control around the generic point, on which we can define the concept of generic radius of convergence. Dwork’s transfer theorem tells us that radius over a disc is \(\ge\) the generic radius of convergence at the boundary.
For \(R\in\{ K\langle t/\beta\rangle, K[[t/\beta]]\}\)