Timeline for Generalizations of 'Injectivity on one line'
Current License: CC BY-SA 3.0
11 events
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| Apr 19, 2018 at 17:05 | comment | added | user237522 | If I am not wrong, algebraic closedness is needed for the implication: $\gamma: t \mapsto (f(t),g(t))$ is injective and $(f'(t),g'(t)) \neq (0,0)$ for all $t \in k$ implies that $\gamma$ is an embedding. (Because, in that case, the D-resultant is a non-zero constant, and then $k[f(t),g(t)]=k[t]$). | |
| Apr 19, 2018 at 17:02 | history | edited | user237522 | CC BY-SA 3.0 |
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| Apr 11, 2018 at 13:58 | history | edited | user237522 | CC BY-SA 3.0 |
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| Apr 11, 2018 at 13:21 | history | edited | user237522 | CC BY-SA 3.0 |
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| Apr 11, 2018 at 9:29 | history | edited | user237522 | CC BY-SA 3.0 |
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| Apr 11, 2018 at 9:20 | history | edited | user237522 | CC BY-SA 3.0 |
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| Apr 11, 2018 at 9:14 | history | edited | user237522 | CC BY-SA 3.0 |
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| Mar 28, 2018 at 0:37 | history | edited | user237522 | CC BY-SA 3.0 |
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| Mar 27, 2018 at 17:37 | comment | added | Takumi Murayama | Regarding Question 1, the Abhyankar–Moh theorem is valid over any field of characteristic zero, and there is even a version over positive characteristic fields that puts conditions on exponents; see the Main Theorem in Abhyankar and Moh's original paper. The result by J. Lang cited by Gwoździewicz does not need the field to be algebraically closed. Did you find where Gwoździewicz needs that assumption? | |
| Mar 25, 2018 at 4:58 | history | edited | user237522 | CC BY-SA 3.0 |
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| Mar 25, 2018 at 4:41 | history | asked | user237522 | CC BY-SA 3.0 |