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The term Galois representation is frequently used when the G-module is a vector space over a field or a free module over a ring, but can also be used as a synonym for G-module. The study of Galois modules for extensions of local or global fields is an important tool in number theory.
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Benedict Gross's paper on companion forms
In the page 458 of his paper(A tameness criterion for Galois representations associated to modular forms), Gross wrote the following
"A detailed analysis of $U_p(Af)+V_p(<p>f)$ shows that it
vanishes …