Timeline for Reduction theory of higher dimensional algebraic varieties
Current License: CC BY-SA 4.0
3 events
| when toggle format | what | by | license | comment | |
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| Jan 31, 2021 at 16:02 | comment | added | Will Sawin | Even in characteristic $0$, a good theory of a minimal model does not exist in general, and when it does, it is not necessarily regular (the "minimal model program" instead uses other, less restrictive, conditions on the singularities). The situation is even less clear in characteristic $p$ and less clear than that in mixed characteristic. | |
| Jan 31, 2021 at 16:01 | comment | added | Will Sawin | A closely related problem is finding minimal regular models for singular algebraic varieties. The relation is direct in the case when $K$ is an equal characteristic local field, as then schemes over $\mathcal O_K$ can be spread out to families of varieties over a curve, and usually the mixed characteristic local field is harder than the equal characteristic case. The existence of any regular model at all is unknown in characteristic $p$, but known for surfaces (i.e. curves over a curve). | |
| Jan 31, 2021 at 15:20 | history | asked | Dubious | CC BY-SA 4.0 |