Let $k$ be a field of characteristic $p > 0$. Let $K$ be an extension field of $k$. Let $k^{p^{-\infty}}$ be the perfect closure of $k$. Then Spec($K\otimes_k k^{p^{-\infty}}$) is a one element set?
On Spec($K\otimes_k k^{p^{-\infty}}$)
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$\begingroup$
commutative-algebra
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1http://mathoverflow.net/questions/29935/question-about-tensor-of-two-fields – 2012-12-04
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0@YACP Thanks. As for the Mariano's answer, I don't have the Jacobson's book at hand. As for the Georges' answer, I think it's a bit overkill, though the Grothendieck's formula is interesting. I like the Robin Chapman's answer most. I don't know why he got only one upvote. – 2012-12-04
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3@Makoto Kato: Robin obviously didn't get more than one upvote because people like you didn't upvote him... – 2012-12-04
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0I could not log in MathOverflow at that time so I could not upvote for Robin Chapman. I have no idea why my comment saying so was removed by a moderator. By the way, I already upvoted for him. – 2013-10-22