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Projective bundle formula for derived cobordism

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KA2W01 - Algebraic K-theory, motivic cohomology and motivic homotopy theory

In this talk, I will outline the proof of what I consider to be the the main result of my thesis: the projective bundle formula for derived algebraic cobordism. Derived algebraic cobordism is a geometrically defined cohomology theory of schemes, which generalizes the algebraic cobordism of Levine and Morel in two ways: (1) it is defined for singular schemes (2) that are not necessarily of finite type over a field of characteristic 0. We will also briefly outline the most important consequences of this result: the existence of cobordism Chern classes and an analogue of the Conner—Floyd theorem, which allows us to recover the zeroth algebraic K-theory group of a scheme from its cobordism ring.Some of the results of this talk are results of (separate) collaborations with Shoji Yokura and Ryomei Iwasa.

This talk is part of the Isaac Newton Institute Seminar Series series.

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