Timeline for $F_q×1$-stable affine subspace
Current License: CC BY-SA 4.0
4 events
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| Jun 9, 2022 at 5:39 | comment | added | Piotr Achinger | @Libli right, it does not. And one can probably also imitate proof (T) here directly, by picking a basis of $A$ and $B$ in such a way that the matrix of $B\to A$ is of the form $[ {\rm Id}_d | \ast ]$. In more sophisticated language, the previous hint uses the Plucker embedding of the Grassmannian, while this one uses standard affine charts on the Grassmannian. | |
| Jun 8, 2022 at 21:16 | comment | added | Libli | @PiotrAchinger : do we really need Noether-Hilbert's 90 in the 1-dimensional case? This question mathoverflow.net/questions/418349/… shows that a fairly trivial proof exists in this case. | |
| Jun 8, 2022 at 10:36 | comment | added | Piotr Achinger | Hint: do the case of a one-dimensional linear subspace first (you will need Hilbert's theorem 90). For a linear subspace of dimension $d$, reduce to the previous case using $\bigwedge^d$. For affine subspaces, add one extra coordinate $x$ and put everything in the $x=1$ plane. | |
| Jun 8, 2022 at 1:20 | history | asked | fool rabbit | CC BY-SA 4.0 |