Timeline for Does there exist a point $ x $ of an affine toric variety $ U_{\sigma} $ such that $ x $ is not compatibly split?
Current License: CC BY-SA 4.0
7 events
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| Jan 13, 2023 at 5:12 | comment | added | Schemer1 | Thank you again @KarlSchwede! | |
| Jan 13, 2023 at 1:44 | comment | added | Karl Schwede | This isn't too hard, one way to see it is that there's exactly one Frobenius splitting on an elliptic curve (remember, Frobenius splittings are all global sections of $H^0(X, (1-p)K_X)$ which is 1-dimensional for an elliptic curve). Then one can observe that that particular splitting isn't compatible. There's a couple different ways to do it. For instance, this particular splitting is the canonical map $F_* \omega_X \to \omega_X$ which is never compatible with anything if $X$ is nonsingular. | |
| Jan 12, 2023 at 23:30 | comment | added | Schemer1 | How do we know that an ordinary elliptic curve is not compatibly split at any point? | |
| Jan 12, 2023 at 17:57 | comment | added | Schemer1 | Thank you @KarlSchwede! | |
| Jan 12, 2023 at 17:52 | vote | accept | Schemer1 | ||
| Jan 12, 2023 at 4:13 | history | edited | Karl Schwede | CC BY-SA 4.0 |
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| Jan 12, 2023 at 3:24 | history | answered | Karl Schwede | CC BY-SA 4.0 |