Talk:Kähler differential
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Untitled
[edit]It's unclear whether we're talking about R-modules or S-modules here, it seems like one or the other is a typo. The Kahler differential Omega_{S/R} is an R-module, right?
It's both; In the first contruction given it is explicitly an S-module and becomes an R-module via the homomorphism φ from R to S. In the second method it is explicitly constructed as an R-module and then it is usually shown (although the wikipedia page doesn't show this) that it can be made into an S-module in a canonical way. Although Omega_{S/R} is an S-module, d is only a homomorphism of R-modules. 69.234.35.181 (talk) 21:39, 26 May 2008 (UTC)
I updated the section on the isomorphism of Hom and Der to be more precise, but the universal property of d:S \to \Omega really needs to be made more explicit earlier in the article. Also the 'field' probably shouldn't be labeled as analysis.
Hmw13 (talk) 02:16, 17 September 2009 (UTC)
Examples
[edit]This page should have examples of
- sequence from a quotient algebra
- sequence from a morphism of algebras
- examples of universal derivation composed with a morphism to get a derivation — Preceding unsigned comment added by 97.122.75.155 (talk) 05:35, 2 August 2017 (UTC)
Period Matrices
[edit]There should be an expanded discussion of periods and period matrices. One good place to look for algebraic plane curves is section 2.9 of "Computational Approach to Riemann Surfaces" which uses Newton polygons. — Preceding unsigned comment added by 2601:280:8105:3861:E0ED:C072:9394:186F (talk) 00:20, 14 July 2018 (UTC)