Timeline for Exactness on rational points of algebraic groups
Current License: CC BY-SA 3.0
16 events
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Feb 25, 2015 at 17:53 | comment | added | m07kl | Dear Professor Borovoi: Thanks very much for your patience | |
Feb 25, 2015 at 16:39 | comment | added | Mikhail Borovoi | In characteristic 0 any morphism is separable and any isogeny is central. | |
Feb 23, 2015 at 21:51 | comment | added | m07kl | Sorry, I I meant Corollary 3.20 in Tits's paper. | |
Feb 23, 2015 at 9:30 | history | edited | Mikhail Borovoi | CC BY-SA 3.0 |
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Feb 23, 2015 at 8:34 | vote | accept | m07kl | ||
Feb 23, 2015 at 6:05 | comment | added | Mikhail Borovoi | Since you write "Thank you for your answer", consider upvoting the answer. | |
Feb 23, 2015 at 6:01 | comment | added | Mikhail Borovoi | The paper of Tits on abstract homomorphisms is not relevant here: you deal with algebraic homomorphisms. | |
Feb 23, 2015 at 5:54 | comment | added | Mikhail Borovoi | The image of a homomorphism of algebraic groups is regarded over an algebraic closure. It is Zariski closed, see Borel's book. By definition, an isogeny is is a surjective homomorphism of algebraic groups with finite kernel. | |
Feb 23, 2015 at 5:47 | history | edited | Mikhail Borovoi | CC BY-SA 3.0 |
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Feb 22, 2015 at 22:39 | comment | added | m07kl | Dear Professor Borovoi: Please also see section 3.18 on page 515 in jstor.org/stable/1970833?seq=1#page_scan_tab_contents | |
Feb 22, 2015 at 22:23 | comment | added | m07kl | Dear Mikhail: why (im$\phi$)(k) is closed in $F(k)$? I think im$\phi$(k) is not Zariski closed in F(k) in general, in my case im$\phi$(k) is in fact Zariski dense in F(k), because it has finite index. It follows from Proposition 3.19 of [3] we need homomorphism to be central and surjective. However, I don't know whether they only talk about affine algebraic groups and whether the isogeny $\phi:(\tilde{G}\times G_{ant})/U \rightarrow G$ is central and separable? [3] jstor.org/stable/1970833?seq=1#page_scan_tab_contents | |
Feb 22, 2015 at 20:56 | history | edited | Mikhail Borovoi | CC BY-SA 3.0 |
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Feb 22, 2015 at 20:28 | history | edited | Mikhail Borovoi | CC BY-SA 3.0 |
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Feb 22, 2015 at 19:28 | comment | added | m07kl | Dear Mikhail. Thank you for your answer and I will reply soon. BTW, the algebraic groups, I talk about, are not necessarily affine. | |
Feb 22, 2015 at 18:48 | history | edited | Mikhail Borovoi | CC BY-SA 3.0 |
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Feb 22, 2015 at 18:32 | history | answered | Mikhail Borovoi | CC BY-SA 3.0 |