Erratum to "Slope filtration for relative Frobenius" (28 Apr 2011)

There are two minor errors in the statement of Proposition 3.3.2.

1. The module $M$ should not be assumed to be a $\phi$-module, but only
a module equipped with an isomorphism $\phi^* M \cong M$. That is,
we should not assume $M$ is finite free over $R$. That is because
in the proof of Theorem 3.1.3, we take $R = \mathcal{R}^{\mathrm{bd}}$ and
$S = \tilde{\mathcal{R}}_L^{\mathrm{bd}}$, and the module $M$ is the 
restriction of scalars of a $\phi$-module over $\mathcal{R}$. 

2. We may not conclude that $N$ is a $\phi$-module, only a 
finite *locally* free module equipped with an isomorphism
$\phi^* N \cong N$. 
(The descent of $N$ as a module is given by SGA1, Expose VIII, Corollaire 1.3;
the action of $\phi$ is given by op. cit., Corollaire 1.2, and the finite
local freeness by op. cit., Proposition 1.10.) 
However, if $R$ is a Bezout domain, then any finite locally free module 
is free (Remark 1.1.2); so Theorems 3.1.2 and 3.1.3 are not affected.

Additional corrections:

-- Ruochuan Liu points out that Definition 2.2.4 should also include the
condition that sup_i {|a_i| e^{-ri}} is finite.

-- Remark 2.2.5 only applies when K has positive residual characteristic.
If K has characteristic 0, one must instead recopy the proofs from [22]
to see that the extended Robba ring has the desired properties.