The yoga of schemic Grothendieck rings, a topos-theoretical approach
arXiv:1004.4260
Abstract
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.
arXiv commentThis is the companion to "Schemic Grothendieck rings and motivic rationality" (arXiv:0910.0684), renamed henceforth "The dogma of schemic Grothendieck rings, a model-theoretic approach", but entirely from a topos-theoretical point of view.