On Grothendieck's Riemann-Roch Theorem

2016/03/22 by Alberto Navarro, Navarro, Alberto
Mathematics · #14C40 #19E20 #Algebraic Geometry (math.AG) #FOS: Mathematics #K-Theory and Homology (math.KT) #math.AG #math.KT #msc:14C40 #msc:19E20

paper · pdf · doi:10.48550/arxiv.1603.06740

18 pages

arxiv created 2016/03/22 · arxiv updated 2016/03/23

Abstract

We prove that, for smooth quasi-projective varieties over a field, the K-theory K(X) of vector bundles is the universal cohomology theory where c₁(L⊗ L)=c₁(L)+c₁( L)-c₁(L)c₁( L). Then, we show that Grothendieck's Riemann-Roch theorem is a direct consequence of this universal property, as well as the universal property of the graded K-theory GK^\bullet (X)⊗ ℚ.

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