Timeline for Two (other) rings...are they isomorphic?
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| Nov 12, 2014 at 22:00 | comment | added | Nicholas Proudfoot | Thanks, this is a great idea! In fact, I would be happy producing an etale map from Spec(R) to Spec(S). Since etale is equivalent to inducing an isomorphism on tangent cones, any homomorphism from R to S of the form $x_i\mapsto x_i + \text{higher order}$ would do the trick. When $n=2$, your approach of sending $x_i$ to $x_i + \frac{1}{n(n-1)} e_1 x_i - \frac{1}{n}x_i^2$ does this perfectly on the first try. When $n=3$, this doesn't quite work; a second step is required. But the idea seems very promising! | |
| Nov 12, 2014 at 20:03 | history | answered | Vladimir Dotsenko | CC BY-SA 3.0 |