Timeline for Betti sequence of finite dimensional commutative algebras
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Nov 14, 2019 at 16:58 | comment | added | Hailong Dao | Also, note that it is easy to give sequence $(c_i)$ with no $A$. For instance, we know that it has to be eventually non-decreasing. Or, if it is eventually constant, then $A$ is a hypersurface and the sequence has to be constant from the beginning. So, a lot of constraints would have to be added to avoid trivial examples. | |
| Nov 14, 2019 at 16:11 | comment | added | Hailong Dao | Even when $k$ is small, one can get examples of infinitely many local $A$ by looking at complete intersections. Say $I=(x^2+f, y^2+g)$ for $f,g$ of high degrees. | |
| Nov 14, 2019 at 15:51 | comment | added | Mare | Thanks, another question might be what about countable fields such as $k= \mathbb{Q}$ and whether there might exist a non-constant sequence $(c_i)$ where only finitely many algebras exist even for uncountable fields. | |
| Nov 14, 2019 at 15:49 | history | edited | Hailong Dao | CC BY-SA 4.0 |
added 8 characters in body
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| Nov 14, 2019 at 15:39 | history | answered | Hailong Dao | CC BY-SA 4.0 |