MATH Seminar
| Title: More examples of non-rational adjoint groups |
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| Seminar: Algebra |
| Speaker: Nivedita Bhaskhar of Emory University |
| Contact: David Zureick-Brown, dzb@mathcs.emory.edu |
| Date: 2014-01-21 at 4:00PM |
| Venue: W302 |
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| Abstract: A k-variety is said to be rational if its function field is purely transcendental over k. The first example of a non-rational adjoint k-group PSO(q) was given by Merkurjev as a consequence of his computations of R-equivalence classes of adjoint classical groups. The quadratic form in question has non-trivial discriminant which property is used crucially in the proof. Gille provided the first example of a quadratic form of trivial discriminant whose associated adjoint group is non-rational. In this talk we give a recursive construction to produce examples of $k_n$-quadratic forms $q_n$ in the n-th power of the fundamental ideal in the Witt ring whose corresponding adjoint groups PSO($q_n$) are not (stably) rational. |
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