All Questions
Tagged with frobenius-map ac.commutative-algebra
7 questions
3
votes
0
answers
192
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How can I prove this stronger version of Fedder's Criterion?
I was reading Fedder's original paper which proved what is now known as "Fedder's criterion". I noticed that the abstract stated something which is a priori stronger than what is proved in ...
- 317
2
votes
1
answer
160
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Finding the mistake in an argument concerning $F$-finite $F$-split local Cohen--Macaulay ring of dimension $1$
Let $R$ be a commutative Noetherian ring, and $\phi: R \to R$ be a ring homomorphism. For an $R$-module $M$, let $^{\phi}M$ be the $R$-module defined via restriction of scalars via $\phi$, i.e., as ...
- 20.5k
1
vote
0
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82
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Relative 1 form of Frobenius morphism
Let $X$ be a connected smooth algebraic variety over a field $k$ of characteristic $p > 0$. We can consider the Frobenius morphism associated to $X \mapsto Spec(k)$. I'd like to show $\Omega^{1}_{X/...
- 73
1
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If $ n \in \mathbb{N} $, then does the Reynolds operator of $ \mathbb{G}_{m}^{n} $ commute with the Frobenius endomorphism?
If $ n \in \mathbb{N} $, then $ \mathbb{G}_{m}^{n} $ is linearly reductive. Let $ \beta: \mathbb{G}_{m}^{n} \to \operatorname{GL}(\mathbf{V}) $ where $ \mathbf{V} $ is a vector space over an ...
- 912
1
vote
1
answer
149
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When is $R$ a direct summand of Frobenius pushforwards?
Let $(R,\mathfrak m)$ be a reduced Noetherian local ring of prime characteristic $p$. For integer $e>0$, let $F^e_* R$ denote the $R$-module which is $R$ as an abelian group, but the $R$-module ...
- 20.5k
4
votes
0
answers
189
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If the Frobenius endomorphism of a characteristic $p$ ring is epimorphic, is it surjective?
MO question 19282 is about integral epimorphisms of commutative rings, and a counterexample is given to surjectivity. What about the case of the Frobenius endomorphism of a commutative, characteristic ...
- 4,492
2
votes
1
answer
195
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Length of a module and Frobenius map
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 ...
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