Timeline for Terminology for vanishing of Hochschild homology with symmetric coefficients?
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Nov 5, 2015 at 15:45 | comment | added | Yemon Choi | @MannyReyes Thanks for the reminder. Once upon a time I used to remember Harrison's paper and all that Barr-Gerstenhaber-Schack jazz: arxiv.org/abs/0709.3325 (see the list of references) | |
| Nov 5, 2015 at 15:21 | comment | added | Manny Reyes | Not an answer, but to confirm that "commutative Hochschild homology" is possibly not the best term: The phrase "commutative cohomology" was used by Harrison (1962) for a symmetrized version of Hochschild cohomology over a commutative ring. On the other hand, my understanding is that this and its homological variant have since been called "Harrison (co)homology," as in the following, for instance: sciencedirect.com/science/article/pii/0021869368900628 | |
| Nov 5, 2015 at 12:50 | history | edited | Yemon Choi | CC BY-SA 3.0 |
tweaked to make it clearer what my actual question is
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| Nov 3, 2015 at 0:22 | comment | added | Yemon Choi | @anon That is all very well, but it doesn't answer my actual question. If I just wanted to know how to write a generic title for a paper I would go and look at my back catalogue | |
| Nov 3, 2015 at 0:13 | comment | added | anon | The rule of thumb is that a title shouldn't be more than 9 words. Save the more precise statements for the abstract. | |
| Nov 2, 2015 at 18:47 | comment | added | Tyler Lawson | @YemonChoi Ach, that's because I confused Kahler differentials with the cotangent complex; so formally smooth of dimension 1 instead. Sorry. | |
| Nov 2, 2015 at 18:28 | comment | added | Yemon Choi | @TylerLawson I'm always uncertain which things are definitions and which are results. Smooth means $H^2_s(A,M)=0$ for all commutative $M$, I think? FWIW I'm getting all of $H_2(A,M)=0$, which wouldn't happen for e.g. $k[x,y]$ even though that is smooth | |
| Nov 2, 2015 at 18:02 | comment | added | Vidit Nanda | I don't have an answer, but +1 for wanting to change that title. For what it is worth, it is entirely reasonable to say $A$ is $n$-acyclic with $M$-coefficients if $H_k(X;M) = 0$ for all $k \geq n$. So maybe "2-acyclicity of a commutative Banach algebra in Hochschild homology with symmetric coefficients"? | |
| Nov 2, 2015 at 17:53 | comment | added | Tyler Lawson | I will leave the (likely unhelpful) comment that I believe this is equivalent to the concept of being "formally smooth" in the world of ordinary homological algebra that I know. Based on your last sentence you may know this. | |
| Nov 2, 2015 at 17:10 | history | asked | Yemon Choi | CC BY-SA 3.0 |