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Results tagged with diophantine-geometry
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user 5101
2
votes
Accepted
How should multiplicative height on projective space interact with automorphisms?
The naive height is not at all intrinsic. It is just a convenient choice to work with for notational simplicity. If one is doing things properly one should be counting rational points of bounded heigh …
- 21.4k
7
votes
Accepted
Obstruction to rationality of del Pezzo surfaces of degree 4
Interesting question.
But, alas, the answer is no.
The issue is that you have missed an extra non-rationality criterion. Namely, it is possible that such a surface $X$ has $\mathrm{Br}(X) = \mathrm{ …
- 21.4k
5
votes
How can the number of rational points depend on the choice of height function?
Surely this behaviour can never happen, but it will be near impossible to prove this. Conjectures of Manin and others predict that there is an asymptotic formula for these functions in many cases, and …
- 21.4k