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Finding the mistake in an argument concerning $F$-finite $F$-split local Cohen--Macaulay rin...

@uno, you are correct in the comments above, $F^e_*(-)$ is not $R$-linear. In particular, the mistake is the line right here: The exact sequence $0\to R \xrightarrow{x} R\to R/xR\to 0$ then gives ri …
Karl Schwede's user avatar
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Does there exist a point $ x $ of an affine toric variety $ U_{\sigma} $ such that $ x $ is ...

Actually, on an affine variety, if it is $F$-split, then it is compatibly $F$-split with every point (possibly changing the splitting). This is not true in the projective case (an ordinary projective …
Karl Schwede's user avatar
  • 20.5k