Some time ago the journal "Algebra and Analysis" (English translation is published in
"St. Petersburg Mathematical Journal") had a special section which was called "easy readings for professional mathematicians", which tried to present in accessible and interesting way some ideas. It seems now t...
Let $(R,m)$ be a Regular local ring of dimension $d$ and char $p>0.$ Let $F^e:R\longrightarrow R$ defined by $r\longrightarrow r^{p^e}$be the Frobenius map.
How to compute $l(R/m^{[p^e]})?.$
I know the answer is $p^{ed}$ but I do not know how to prove it.
I guess they might be useful - but I'll wait a bit to see whether I'll get some feedback here in chat or whether somebody removes the new tags. (Which I'll take as a signal that they are probably not considered useful.)
I suppose the tag-wikis can be mostly copied from the corresponding tags on Mathematics Meta. (Which I can do - but I'll wait first a bit to see whether the new tags are not going to be removed.)
Let $(R,m)$ be a Regular local ring of dimension $d$ and char $p>0.$ Let $F^e:R\longrightarrow R$ defined by $r\longrightarrow r^{p^e}$be the Frobenius map.
How to compute $l(R/m^{[p^e]})?.$
I know the answer is $p^{ed}$ but I do not know how to prove it.
