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Rigid analytic methods in tropical geometry (and vice-versa)
Fri, October 9, 2009 2:00PM - 3:00PM
| Time: | 2:00PM - 3:00PM |
| Location: | Baker Board Room #245 |
| Speakers: | Joe Rabinoff, Joe Rabinoff |
| Abstract: | A small deformation of a tropical variety corresponds in algebraic geometry to a rigid-analytic deformation of an algebraic variety. For example, a deformation of the tropicalization of the polynomial x+y-1 over a non-Archimedean field K would correspond to a polynomial ax + by + c, where |a-1|, |b-1|, and |c-1| are small; these not algebraic conditions on a,b, and c, but are open conditions in the rigid-analytic sense. I will give a brief introduction to the theory of rigid geometry, which closely paralells the theory of finite-type schemes over a non-Archimedean field, and then I will give an indication of how such methods can be used to prove a deformation-invariance result for tropical intersection numbers using a corresponding result in rigid geometry. |
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