Timeline for group structure on (subsets of) tropicalizations of Abelian varieties
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 11, 2014 at 6:20 | vote | accept | Dima Sustretov | ||
| Jun 7, 2014 at 13:45 | comment | added | ACL | Yes and no. This question of comparing the skeleton of the elliptic curve (the canonical circle described above) with more naïve tropicalizations from embeddings is discussed in a paper of Baker, Payne and Rabinoff, Nonarchimedean geometry, tropicalization, and metrics on curves, arxiv.org/abs/1104.0320. | |
| Jun 6, 2014 at 21:59 | comment | added | Dima Sustretov | so when one takes $K^\times$ and apply valuation to its factor by $q$, is it possible to somehow relate the quotient to the image of the valuation map composed with some embedding of the quotient elliptic curve (or rather an open subset thereof) into $\mathbb{G}_m^2$, say? | |
| Jun 6, 2014 at 21:40 | comment | added | ACL | Tropicalizing just means applying the valuation map, once it makes sense. The case of semistable formal schemes also gives rise to maps to simplicial complexes associated with the special fiber, but this is a (related but) different story. | |
| Jun 6, 2014 at 21:06 | comment | added | Dima Sustretov | Thanks for this detailed answer! You have mentioned that as $K^\times$ tropicalises to $\mathbb R$, the quotient tropicalizes to $\mathbb{R}/\mathbb{Z}\mathrm{log}|q|$. What do you mean by "tropicalizes" here? I encountered the following usage of this word: embed into into a torus, then apply valuation map, but it looks like here the map is something else? | |
| Jun 6, 2014 at 19:42 | history | answered | ACL | CC BY-SA 3.0 |