Timeline for How to compute the $G$-theory groups of $k[x,y]/(xy)$ for any field $k$
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Feb 28, 2022 at 2:42 | comment | added | Boris | Thank you very much for your kind guidance and explanations. | |
| Feb 28, 2022 at 2:41 | comment | added | user127776 | I suggest to check the proof of homotopy invariance of $G$-theory, you might be able to apply some modification of that idea to directly show that the homomorphism above is a split injection. | |
| Feb 28, 2022 at 2:41 | comment | added | Boris | I see. Thank you very much for your kind help and information. | |
| Feb 28, 2022 at 2:39 | comment | added | user127776 | So the calculation suggests that the map $G_n(A)\rightarrow G_n(A_x)$ is a split injection. I am not sure how to show this directly. This reminds me the way we prove that $G$-theory is homotopy invariance. | |
| Feb 28, 2022 at 2:34 | comment | added | Boris | So the boundary map in the $G$-theory localization sequence is defined by the Gysin homomorphism? | |
| Feb 28, 2022 at 2:32 | history | edited | user127776 | CC BY-SA 4.0 |
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| Feb 28, 2022 at 2:30 | comment | added | Boris | How should I understand the boundary map in the $G$-theory localization sequence above? Thanks. | |
| Feb 28, 2022 at 2:29 | comment | added | Boris | Thank you so much for your kind help. | |
| Feb 28, 2022 at 2:22 | history | edited | user127776 | CC BY-SA 4.0 |
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| Feb 28, 2022 at 2:02 | history | answered | user127776 | CC BY-SA 4.0 |