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Does the choice of the algebraically closed field of characteristic $p$ have influence on the module category?

The question is not completely clear about what is meant by a difference. Let me give one interpretation. Every representation of a finite group $G$ over an algebraically closed field is defined over ...
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Completion of infinite degree extension of perfectoid fields is perfectoid?

I'm assuming you mean infinite algebraic extensions, as otherwise there is no standard way of completing them. Let $K$ be a perfectoid field, let $L$ be an infinite algebraic extension. Then $L$ ...
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0 votes

Galois groups vs. fundamental groups

I found this introduction by David Corwin very accessible and well explained: https://math.berkeley.edu/~dcorwin/files/etale.pdf.
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