Timeline for Rational map defined over K leads to algebra question
Current License: CC BY-SA 2.5
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| Jun 29, 2010 at 3:05 | comment | added | BCnrd | It's OK, even w/o perfectness: if char. is $p > 0$ then multiplying $f$ against $f^{p^n - 1}$ for big $n$ yields $f^{p^n}$ with coeffs in $K_ s$ inside $\overline{K}$. In general (any char.), now all coeffs in finite Galois ext'n $L/K$. Multiplying against conj's under non-triv. el'ts of ${\rm{Gal}}(L/K)$ yields $fg$ w/ coeffs lie in $K$. But motivation is misplaced: the def'n you cite is wrong. The right def'n is all $f_i/f_j \in K(V)$ for one $j$ s.t. $f_j \ne 0$. So in final para. $\phi = \psi = [1,1]$. The alg. geom. in AEC is clunky; it will all become cleaner when you learn schemes. | |
| Jun 29, 2010 at 2:43 | history | asked | warsamekei | CC BY-SA 2.5 |