Timeline for Vector space structure of the Zariski tangent space
Current License: CC BY-SA 4.0
17 events
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| Apr 14, 2021 at 16:00 | comment | added | hm2020 | @Gabriel - in the link you find some details on how to construct the enveloping algebra $U(Lie(G))$ and $k\oplus Lie(G)$ in terms of the group scheme $G$ - maybe this is helpful. | |
| Apr 14, 2021 at 15:35 | comment | added | Gabriel | Dear @hm2020, thank you for your answer. Even though I found it really hard to understand and I didn't understand the relation between some things you say and the question I asked, it was indeed helpful. | |
| Apr 14, 2021 at 11:25 | history | edited | hm2020 | CC BY-SA 4.0 |
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| Apr 14, 2021 at 10:45 | history | edited | hm2020 | CC BY-SA 4.0 |
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| Apr 14, 2021 at 10:14 | comment | added | hm2020 | @Gabriel - I added a link that may be helpful. | |
| Apr 14, 2021 at 10:11 | history | edited | hm2020 | CC BY-SA 4.0 |
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| Apr 12, 2021 at 10:22 | history | edited | hm2020 | CC BY-SA 4.0 |
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| Apr 11, 2021 at 13:36 | history | edited | hm2020 | CC BY-SA 4.0 |
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| Apr 11, 2021 at 11:02 | history | edited | hm2020 | CC BY-SA 4.0 |
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| Apr 11, 2021 at 10:52 | history | edited | hm2020 | CC BY-SA 4.0 |
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| Apr 8, 2021 at 16:28 | history | edited | hm2020 | CC BY-SA 4.0 |
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| Apr 8, 2021 at 13:06 | history | edited | hm2020 | CC BY-SA 4.0 |
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| Apr 8, 2021 at 12:39 | history | edited | hm2020 | CC BY-SA 4.0 |
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| Apr 8, 2021 at 12:28 | comment | added | Gabriel | [...] it is nothing but $\widetilde{T_p X}$. This is clear from its definition. What I don't understand is its inherited group structure coincides with the vector space structure we're defining. | |
| Apr 8, 2021 at 12:27 | comment | added | Gabriel | Dear @hm2020, bear with me as I try to understand in detail your answer. First of all, your notation seem to imply that you consider a point $p\in X$ and $R=\mathscr{O}_{X,p}$, $I=\mathfrak{m}_{p}$. So your morphism $\psi_\mu:R\to k[\varepsilon]$ induces a map $\operatorname{Spec} k[\varepsilon]\to \operatorname{Spec} R$ and an element of $X(k[\varepsilon])$ by composing with the natural map $\operatorname{Spec} \mathscr{O}_{X,p}\to X$. Is that what you mean? Why are you considering $X$ affine here? Also, if $X$ is a group scheme, I do know the kernel of $X([\varepsilon])\to X(k)$ as a set | |
| Apr 8, 2021 at 11:27 | history | edited | hm2020 | CC BY-SA 4.0 |
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| Apr 8, 2021 at 11:21 | history | answered | hm2020 | CC BY-SA 4.0 |