Timeline for Proofs of the Chevalley-Warning Theorem
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Jul 15, 2017 at 23:39 | comment | added | Anurag | @ZachTeitler: To be precise, for any polynomial $P \in R[t_1, \dots, t_n]$ and any finite subsets $A_1, \dots, A_n \subseteq R$ with the property that difference of two distinct elements in $A_i$ is never a zero divisor of the ring $R$, if $P$ vanishes on all points except one in $A_1 \times \cdots \times A_n$, then $\deg P \geq \sum_{i = 1}^n (|A_i| - 1)$. | |
| Jul 15, 2017 at 23:30 | comment | added | Anurag | Depends on how you want to see this. The result remains valid over any finite grid over a commutative ring with identity as long as it satisfies a certain "condition (D)". That's not true for Ax's lemma which requires properties of finite fields. This lemma is much more general, and it holds because of some very basic properties of polynomials. | |
| Jul 14, 2017 at 17:28 | comment | added | Zach Teitler | Sure, but isn't that a special case of Ax's Lemma which Pete describes as "impressively easy to prove"? | |
| Jul 14, 2017 at 17:24 | history | edited | Anurag | CC BY-SA 3.0 |
added 4 characters in body
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| Jul 14, 2017 at 16:00 | history | edited | Anurag | CC BY-SA 3.0 |
added two new proofs
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Apr 14, 2015 at 20:17 | history | edited | Anurag | CC BY-SA 3.0 |
made some corrections in Proof 6. We need the degree of P to be greater than or equal to the degree of R for the final conclusion.
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| Apr 13, 2015 at 19:09 | history | edited | Anurag | CC BY-SA 3.0 |
added another proof
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| Apr 9, 2015 at 7:47 | history | edited | Anurag | CC BY-SA 3.0 |
Added Proof 5.
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| Apr 9, 2015 at 2:29 | history | answered | Anurag | CC BY-SA 3.0 |