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Grothendieck-Riemann-Roch for derived schemes

Parker Lowrey, Timo Schürg

Number 27
Author Timo Schürg
Year 2012

We define bivariant algebraic K-theory and bivariant derived Chow on the homotopy category of derived schemes over a smooth base. The orientation on the latter corresponds to virtual Gysin homomorphisms. We then provide a morphism between these two bivariant theories and compare the two orientations. This comparison then yields a homological and cohomological Grothendieck-Riemann-Roch formula for virtual classes.

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