Determinants and algebraic K-theory |
Birgit Richter |
Thursday, 2011-12-22 17:00 |
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Algebraic K-theory captures arithmetic properties of rings. The first algebraic K-group of a commutative ring is closely related to the units of the ring via a suitable determinant map. For brave new rings (aka structured ring spectra) such determinant maps do not exist in general: For the algebraic K-theory of the sphere spectrum Waldhausen showed that such a map cannot exist and work of Ausoni-Dundas-Rognes proves a negative result for complex connective K-theory. I will motivate why we would like to have (suitable versions of) determinants and sketch some work in progress joint with John Rognes on that question. |