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Results tagged with characteristic-p
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user 2083
Fields of characteristic $p$, i.e., fields for which there is a prime $p$ such that $px=0$ for each $x$. Do not use this tag for questions on characteristic polynomials of a matrix.
6
votes
Accepted
Frobenius functor and length of local cohomology
Let $p=2$, $R=k[[x,y]]/(x^2,xy)$. Then $H^0_m(R) \cong R/m= k$. $F(k) = R/m^{[2]}= k[[x,y]]/(x^2,xy,y^2)$ has length $3 \neq 2\times 1$.
In general for a finite length module $M$, the condition that …
- 30.6k
6
votes
algorithm for calculating the Chow groups of a variety over a finite field
I am not an expert, but let me point out that computing $CH^0(X)$ (which is freely generated by the irreducible components) is already quite hard. Algorithms do exist in this case, see page 206 of "Id …
- 30.6k
2
votes
Class groups of normal domains over finite fields
I recently found some references: Theorem 4.5 of this paper and Theorem 4 + next Corollary of this paper which says:
If $(R,m,k)$ is a complete normal local domain of dimension $2$ such that $k$ …
- 30.6k
11
votes
2
answers
1k
views
Class groups of normal domains over finite fields
Let R be a local, normal domain of dimension 2. Suppose that R contains a finite field. I am interested in knowing when the class group of R is torsion. In characteristic 0, this is known to be relate …
- 30.6k
5
votes
Have people successfully worked with the full ring of differential operators in characterist...
Dear Matt: The people who are actively working with this whom I know are Genady Lyubeznik and Manuel Blickle.
The key point seems to be that certain $R[F]$-modules become simpler when viewed as $D_R$- …
- 30.6k