Timeline for Application of Frobenius splitting in characteristic $0$
Current License: CC BY-SA 3.0
5 events
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| Nov 8, 2015 at 16:36 | comment | added | meh | I'm not sure this will pass even the 'techniques such as Frobenius splitting' filter, but to me two amazing applications of characteristic p to prove results in characteristic zero are Mori's proof of the Hartshorne conjecture and the Deligne-Illusie (algebraic) proof of Kodaira vanishing | |
| Nov 8, 2015 at 14:56 | comment | added | Jim Humphreys | If you have access to MathSciNet, it may be helpful to check their list of 100+ citations of the Brion-Kumar book. But again I'd stress that the problems solved using Frobenius splitting tend to be solved already in characteristic 0 by more traditional methods. | |
| Nov 8, 2015 at 14:54 | comment | added | Jim Humphreys | Techniques such as Frobenius splitting were introduced in prime characteristic because it's so hard to work out analogues involving geometry or representations of algebraic groups already known in characteristic 0. But there are fruitful interactions between characteristic $p$ questions and quantum groups (often at a root of unity) in characteristic 0, while Frobenius splitting methods have applications to quantum groups; see for instance a paper by Kumar-Littelmann, Algebraization of Frobenius splitting via quantum groups, Ann. of Math. 155 (2002), 491–551. | |
| Nov 8, 2015 at 7:19 | history | edited | GH from MO | CC BY-SA 3.0 |
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| Nov 8, 2015 at 7:15 | history | asked | Ben | CC BY-SA 3.0 |