Geodesic
Leibniz formula in algebraic $K$-theory
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 11, Tome 319 (2004), pp. 264-292

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The paper can be considered as an addendum to a paper of Thomason and Throbaugh where $K$-theory of algebraic varieties is equipped with relative $K$-groups. It is proved that this enriched $K$-theory satisfies the Panin–Smirnov axioms for ring cohomology theories of algebraic varieties. In particular it is proved that the Leibnitz formula, describing an interaction between a multiplication and a differential, holds in this case. A language of symmetric spectra and of monoidal model categories is used. 
@article{ZNSL_2004_319_a9,
     author = {A. L. Smirnov},
     title = {Leibniz formula in algebraic $K$-theory},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {264--292},
     publisher = {mathdoc},
     volume = {319},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2004_319_a9/}
}
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A. L. Smirnov. Leibniz formula in algebraic $K$-theory. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 11, Tome 319 (2004), pp. 264-292. http://geodesic.mathdoc.fr/item/ZNSL_2004_319_a9/