The yoga of schemic Grothendieck rings, a topos-theoretical approach

Details The yoga of schemic Grothendieck rings, a topos-theoretical approach The yoga of schemic Grothendieck rings, a topos-theoretical approach

2010-04-24

arxiv.org/abs/1004.4260v1

Mathematics

Algebraic Geometry

This is the companion to "Schemic Grothendieck rings and motivic rationality" (arXiv:0910.0684), renamed henceforth "The dogma

Scientific paper

We propose a suitable substitute for the classical Grothendieck ring of an algebraically closed field, in which any quasi-projective scheme is represented, while maintaining its non-reduced structure. This yields a more subtle invariant, called the schemic Grothendieck ring, in which we can formulate a form of integration resembling Kontsevich's motivic integration via arc schemes. Whereas the original construction was via definability, we have translated in this paper everything into a topos-theoretic framework.

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