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Kristian Moi: Grothendieck-Witt groups of stable infinity categories

Time: Thu 2019-11-28 10.15 - 12.00

Location: Kräftriket, house 6, room 306 (Cramér-rummet)

Participating: Kristian Moi, KTH

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The algebraic K-groups of a ring \(A\) capture 'additive' algebraic properties of modules over \(A\). In a similar way the lesser known Grothendieck-Witt-groups of \(A\) capture 'additive' algebraic properties of \(A\)-modules with given symmetric bilinear forms on them. A classical example of such an invariant is the signature of a real symmetric bilinear form. This talk is about an extension of Grothendieck-Witt-groups to the world of stable infinity categories. I will discuss the relations of the new Grothendieck-Witt-theory to K-theory and L-theory via the 'fundamental cofibre sequence' and its relations to previous definitions of Grothendieck-Witt-theory. A key feature of the new theory is that we do not need to invert 2 and it can even be applied to ring spectra, not just discrete rings. This is joint work with Calmès, Dotto, Harpaz, Hebestreit, Land, Nardin, Nikolaus and Steimle.