Timeline for Two definitions for smoothness
Current License: CC BY-SA 4.0
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| May 5, 2022 at 9:53 | history | edited | cos_dm_math21 | CC BY-SA 4.0 |
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| May 5, 2022 at 7:27 | comment | added | Z. M | quasi-free is noncommutative. Every ring on SP (as in texts in algebraic geometry) is commutative by default. By the way, formal smoothness coincides with classical smoothness under finiteness. | |
| May 4, 2022 at 19:36 | comment | added | cos_dm_math21 | Also, it seems to me that formally smooth means quasi-free in Weibel's book (page 313), not smooth | |
| May 4, 2022 at 19:07 | comment | added | cos_dm_math21 | What made me think that these definitions are equivalent is that Whitherspoon invoke in the proof of Theorem 3.2.6 (HKR Theorem) a result from Weibel's book on smooth algebras, although she gave a different definition for this notion. | |
| May 4, 2022 at 18:45 | comment | added | Z. M | They do not seem to be equivalent in general. The second is called formally smooth which is satisfied by, say, a polynomial algebra on infinitely many variables. | |
| May 4, 2022 at 18:43 | history | edited | cos_dm_math21 |
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| May 4, 2022 at 18:23 | history | asked | cos_dm_math21 | CC BY-SA 4.0 |