Timeline for field of coefficients, automorphism, cohomology
Current License: CC BY-SA 3.0
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| Feb 15, 2013 at 14:39 | comment | added | Damian Rössler | It is also necessary to extend the scalars. Consider for example the product of a smooth alg. var. $X$ over $k$ with itself $n$-times. Let $h$ act by cyclic permutation of the factors. Then the action of $h$ on $H^1_{\rm dR}$ on the product is up to a sign also by permutation of the $H^1_{\rm dR}$ cohomology groups of $X$. This action cannot be diagonalised on $k$ in general unless you extend the scalars. | |
| Feb 15, 2013 at 9:11 | history | asked | autof | CC BY-SA 3.0 |