Timeline for The Hasse-Weil inequality

5 events

when toggle format	what		by	license	comment
Sep 29 at 19:32	comment	added	John Doyle		Maybe replacing $y^2$ with $y^d$, where $d$ is the degree of $f$, would work.
Sep 29 at 19:13	comment	added	R.P.		I wonder if you can get 0 as a lower bound by tweaking the example. But in any case a lower bound 1 essentially makes the same point.
Sep 29 at 18:52	comment	added	John Doyle		Ah, right, I was implicitly thinking of the points at infinity on the smooth models of the individual curves.
Sep 29 at 18:43	comment	added	R.P.		The phrase "points at infinity" is a bit ambiguous, since it depends on which projective embedding you are thinking of. If you're thinking of $\mathbb{P}^2$, then both curves intersect in the rational point $(0:1:0)$. If you're instead considering the normalization, then you're no longer in $\mathbb{P}^2$, and you might as well take any union of Galois conjugate curves in projective space and perform repeated blow-ups so as to create a disjoint union, which of course never contains a rational point.
Sep 29 at 4:56	history	answered	John Doyle	CC BY-SA 4.0