Timeline for Smoothness of height in Manin conjecture
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Jul 22, 2023 at 15:17 | comment | added | dummy | sent you a follow up email, thank you! | |
| Jul 18, 2023 at 13:50 | comment | added | Daniel Loughran | Feel free to email me if you would like to discuss this in more detail | |
| Jul 18, 2023 at 13:50 | comment | added | Daniel Loughran | Alternatively, there is an approach to going from smooth heights to non-smooth heights by approximating a non-smooth height by a smooth one via some form of the Stone-Weierstrass theorem. I've never seen this written carefully in the literature, but it is closely related to Peyre's idea of equidistribution of rational points in the adelic points. | |
| Jul 18, 2023 at 13:43 | comment | added | Daniel Loughran | Incidently for toric varieties one does not need to assume that the metric is smooth in Poisson summation. This is actually the case in the original papers of Batyrev and Manin on Manin's conjecture for toric varieties, where the natural toric height on projective space is in fact the standard height. | |
| Jul 18, 2023 at 13:42 | comment | added | Daniel Loughran | This is nice question. For additive groups I think that every result in the literature assumes smooth metric at the archimedean places. This is to make the application of Poisson summation easier, but I've no idea whether it is strictly necessary for the method. I think this would be a good exercise to work out for yourself in the case of projective space to see if it works with the standard height. | |
| Jul 14, 2023 at 16:50 | history | edited | YCor |
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| Jul 13, 2023 at 23:57 | history | asked | dummy | CC BY-SA 4.0 |