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Mathematics Seminar Series Abstract
of the Talk by: Dr. Hans Schoutens Ultraproducts in Algebra |
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An
ultraproduct is a tool from logic, and,
unfortunately, scarcely known by algebraists. I will argue for their
usefulness by showing that it can make the "students binomial"
theorem true over the complex numbers: (a+b)^v=a^v+b^v. More precisely, the exponent v in
this magic formula is an ultraproduct of prime
numbers, and therefore defines an endomorphism, called the ultra-Frobenius. Its action on various cohomology
groups is quite extraordinary, and leads to knew characterizations of
rational singularities. I will provide in this talk the general context,
sketch the construction of an ultraproduct, and
state some results. A basic knowledge of algebra should suffice. |
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Address: © 2007 (since August
2007) |