Timeline for Modular functions and integral closure of a valuation ring
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Oct 18, 2019 at 5:20 | comment | added | Shimrod | Why the downvote? I think this is a reasonable Research Question. | |
| Oct 17, 2019 at 16:52 | comment | added | François Brunault | I think the integral closure will be the subring of modular functions of level N which are regular at every point of the preimage of \tau (so the whole orbit of \tau under the SL_2(Z/NZ) action). It is a semi-local ring. | |
| Oct 17, 2019 at 13:51 | comment | added | Shimrod | @JohannesHahn, thanks, I corrected the question. | |
| Oct 17, 2019 at 13:50 | history | edited | Shimrod | CC BY-SA 4.0 |
added 2 characters in body
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| Oct 17, 2019 at 12:27 | comment | added | Johannes Hahn | I think maybe you wanted to ask a slightly different question, because as it is right now, the answer is "no" for trivial reasions: $\mathfrak{o}_\tau$ is uncountable, because it contains $\mathbb{C}$ and $\mathfrak{O}_\tau$ is countable, because it is contained in $F_N$ (which is countable per the description in the linked question). Thus $\mathfrak{O}_\tau$ is not even an extension of $\mathfrak{o}_\tau$, let alone the integral closure. | |
| Oct 17, 2019 at 11:24 | history | asked | Shimrod | CC BY-SA 4.0 |