Answer by Francesco Minnocci for Strengthening Ax-Grothendieck
A version of OP's claim (with an additional hypothesis) is mentioned in a footnote on the first page ofBorel, A. Injective endomorphisms of algebraic varieties. Arch. Math 20, 531–537 (1969)....
View ArticleAnswer by pinaki for Strengthening Ax-Grothendieck
A counterexample for $n = 2$ is the map $(x_1, x_2) \mapsto (x_1x_2 - 1, x_2(x_1x_2 - 1) + x_1)$. This example, which I learned from a paper of Zbigniew Jelonek, was mentioned in an earlier answer of...
View ArticleAnswer by Jason Starr for Strengthening Ax-Grothendieck
Edit. To try and make something productive out of the argument below, let me explain the proof of the Ax-Grothendieck Theorem for affine space using this argument. Also, the argument below includes the...
View ArticleStrengthening Ax-Grothendieck
The question was cross-posted from Math.SE: https://math.stackexchange.com/questions/4566017/strengthening-ax-grothendieckThe question is simple. The Ax-Grothendieck theorem says a polynomial map...
View ArticleClik here to view.
Days of Our Lives’ Tripp and Wendy Leaving Salem Underscores These...
Tripp and Wendy's departure from Salem moved one of the most boring couples off-screen. It didn't have to be this way. Tripp and Wendy had once been dynamic, fascinating characters. Instead of using...
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NCIS Season 21 Episode 9 Review: Prime Cut
Is it time for NCIS: Dallas? Probably not, based on the events of NCIS Season 21 Episode 9. It was a bad week for the franchise, with NCIS: Hawaii being canceled, without warning, after its third...
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The Veil Series Premiere Review: Elisabeth Moss Anchors a Taut Thriller
"The Queen of Peak TV" strikes again. Suffice it to say, beginning with The Veil Season 1 Episode 1, this series premiere was a tour de force in acting, writing, and dialogue.Elisabeth Moss's streak...
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Grey's Anatomy Season 20 Episode 6 Spoilers: Simone Feels Bailey's Wrath &...
Is it time for Richard Webber to hang up the stethoscope permanently? After a bit of a hiatus, we're back to our regularly scheduled program with Grey's Anatomy Season 20 Episode 6, and we're left to...
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CBS Dramas: Our 10 Favorites of the 21st Century
CBS has been reeling fans in with dramas for over 50 years now, and it doesn't look like the network has any plans to stop. The network really has something for everybody in its repertoire, whether...
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Essential Viewing: 11 Glen Powell Movies and TV Shows You Must See
A certain actor has been taking over Hollywood as of late, and his name is Glen Powell. The actor, hailing from Austin, Texas, has a long list of credits to his name, with various appearances on...
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Blue Bloods Season 14 Episode 8 Spoilers: Will Revisiting a Dangerous...
Here we go again.Blue Bloods Season 14 Episode 8 spoilers promise danger for Danny and Baez, thanks to an old enemy. This will likely bring on the suspense, but will it also finally push their...
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Will Trent Season 2 Episode 7 Review: Have You Never Been to A Wedding?
That was an action-packed wedding. Will assumed he was being a good friend by agreeing to escort Faith and Jeremy to a wedding. He never dreamed they'd be fighting for their lives. But, multiple...
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The Good Doctor Season 7 Episode 7 Review: Faith
The Jesus story wasn't as bad as it could have been. Spoilers for The Good Doctor Season 7 Episode 7 made it seem like this would be a ridiculous story, but by halfway through the hour, "Jesus" had...
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The Rookie Season 6 Episode 7 Review: Crushed
The first step in fixing a problem is acknowledging that there is one and getting help. Tim Bradford is on the path to doing that after everything that has happened to him, and Blair is the person...
View ArticleAnswer by Francesco Minnocci for Strengthening Ax-Grothendieck
A version of OP's claim (with an additional hypothesis) is mentioned in a footnote on the first page ofBorel, A. Injective endomorphisms of algebraic varieties. Arch. Math 20, 531–537 (1969)....
View ArticleAnswer by pinaki for Strengthening Ax-Grothendieck
A counterexample for $n = 2$ is the map $(x_1, x_2) \mapsto (x_1x_2 - 1, x_2(x_1x_2 - 1) + x_1)$. This example, which I learned from a paper of Zbigniew Jelonek, was mentioned in an earlier answer of...
View ArticleAnswer by Jason Starr for Strengthening Ax-Grothendieck
Edit. To try and make something productive out of the argument below, let me explain the proof of the Ax-Grothendieck Theorem for affine space using this argument. Also, the argument below includes the...
View ArticleStrengthening Ax-Grothendieck
The question was cross-posted from Math.SE: https://math.stackexchange.com/questions/4566017/strengthening-ax-grothendieckThe question is simple. The Ax-Grothendieck theorem says a polynomial map...
View ArticleClik here to view.
Should The Bear Season 3 Ditch the Cameos & Get Back to Basics?
The Bear is one of those rare stories that comes along once in a blue moon. It doesn't get by on flashy CG, explosions, or modded-out race cars flying down the streets. Witty dialogue, high stress,...
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Sugar Season 1 Episode 6 Review: Go Home
No, life isn’t always like a movie, but if you watch enough of them, you can find a film that often ties into your life. For John on Sugar Season 1 Episode 6, it was Night of the Hunter, starring...
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