Timeline for On rational points of conics

5 events

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Oct 18, 2013 at 11:23	history	edited	Hugo Chapdelaine	CC BY-SA 3.0	I corrected a mathematical typo
Aug 7, 2011 at 21:35	comment	added	Pete L. Clark		@Hugo: okay, sounds good. At this point I have written the last sentence in my above comment so many times in my own work that I have stopped thinking about it. Sorry that I didn't recognize your proof of that above.
Aug 7, 2011 at 1:00	comment	added	Hugo Chapdelaine		Hi Pete, I guess that I had to reprove for myself that if $D$ (a divisor defined over $K$) has degree $1$ on a rational curve then necessarily it is equivalent to an effective divisor of degree $1$ defined over $K$ was not completely obvious to me, but I agree that it is fairly straightforward once you think about it.
Aug 6, 2011 at 21:53	comment	added	Pete L. Clark		@Hugo: I think you are making this a bit more complicated than is necessary. A smooth projective genus zero curve $C_{/K}$ has a $K$-rational divisor of degree $2$: the anti-canonical divisor. If it also has an $L$-rational point with $[L:K] = 2k+1$, then the trace from $L$ down to $K$ is a $K$-rational divisor of degree $2k+1$. Since $2$ and $2k+1$ are relatively prime, we get a $K$-rational divisor $D$ of degree $1$. Since the genus is zero, Riemann-Roch implies that $D$ is equivalent to an effective divisor of degree $1$.
Aug 6, 2011 at 21:07	history	answered	Hugo Chapdelaine	CC BY-SA 3.0