Timeline for rationality of residues of differentials
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 25, 2015 at 16:42 | comment | added | abx | If you apply the trace to the example given in the answer, you find 0, which is compatible with the residue theorem but not very interesting. | |
| Jun 25, 2015 at 15:24 | comment | added | zyx | Jason, thanks for trying to clarify this! I was also confused about what it is written in Serre's book. | |
| Jun 25, 2015 at 15:22 | comment | added | Jason Starr | Hey ... wait a minute! According to Tate's "Residues of Differentials on Curves", the residue is always defined to be an element of $k$. I guess that Tate builds the trace into his definition of the residue. | |
| Jun 25, 2015 at 14:54 | comment | added | Jason Starr | I agree with your computation. But I am confused about how this jibes with the Residue Theorem as stated, for instance, on p. 15, Proposition 6 of Serre's "Algebraic Groups and Class Fields". To extend the Residue Theorem over non-closed fields, presumably at some point we need to take traces. | |
| Jun 25, 2015 at 14:31 | comment | added | Count Dracula | I used the definition of the residue. | |
| Jun 25, 2015 at 14:27 | comment | added | zyx | Could you give more details about how you computed it? | |
| Jun 25, 2015 at 14:21 | history | answered | Count Dracula | CC BY-SA 3.0 |