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Multiplicative Structures on Algebraic K-Theory
Published 2017“…The algebraic $K$-theory of Waldhausen $\infty$-categories is the functor corepresented by the unit object for a natural symmetric monoidal structure. …”
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On the algebraic K-theory of higher categories
Published 2017“…As applications of this technology, we study the algebraic K-theory of associative rings in a wide range of homotopical contexts and of spectral Deligne–Mumford stacks.…”
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Algebraic K-theory with coefficients of cyclic quotient singularities
Published 2017“…In this note, by combining the work of Amiot–Iyama–Reiten and Thanhoffer de Völcsey–Van den Bergh on Cohen–Macaulay modules with the previous work of the author on orbit categories, we compute the algebraic K-theory with coefficients of cyclic quotient singularities.…”
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Spectral Mackey functors and equivariant algebraic K-theory (I)
Published 2019“…We also study fully functorial versions of A-theory, upside-down A -theory, and the algebraic K-theory of derived stacks.…”
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A¹-homotopy invariance of algebraic K-theory with coefficients and du Val singularities
Published 2018“…Weibel, and Thomason and Trobaugh, proved (under some assumptions) that algebraic K-theory with coefficients is A1-homotopy invariant. …”
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A¹-homotopy invariants of corner skew Laurent polynomial algebras
Published 2018Subjects: “…Corner skew Laurent polynomial algebra, Leavitt path algebra, algebraic K-theory, noncommutative mixed motives, noncommutative algebraic geometry…”
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An analogue of Serre’s conjecture for a ring of distributions
Published 2020-07-01Subjects: Get full text
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Additive invariants of toric and twisted projective homogeneous varieties via noncommutative motives
Published 2017“…Later, Merkurjev and Panin described the algebraic K-theory of toric varieties as a direct summand of the algebraic K-theory of separable algebras. …”
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Additive invariants of orbifolds
Published 2020“…Keywords: orbifold; algebraic K–theory; cyclic homology; topological Hochschild homology; Azumaya algebra; standard conjectures; noncommutative algebraic geometry…”
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Equivariant noncommutative motives
Published 2018“…This theory provides a well-adapted framework for the study of G-schemes, Picard groups of schemes, G-algebras, 2-cocycles, G-equivariant algebraic K-theory, etc. Among other results, we relate our theory with its commutative counterpart as well as with Panin’s theory. …”
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On the Cartan map for crossed products and Hopf-Galois extensions
Published 2007“…We study certain aspects of the algebraic K-theory of Hopf-Galois extensions. We show that the Cartan map from K-theory to G-theory of such an extension is a rational isomorphism, provided the ring of coinvariants is regular, the Hopf algebra is finite dimensional and its Cartan map is injective in degree zero. …”
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Invariants of Noncommutative Projective Schemes
Published 2020“…In this note we compute several invariants (e.g. algebraic K-theory, cyclic homology and topological Hochschild homology) of the noncommutative projective schemes associated to Koszul algebras of finite global dimension.…”
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