Comparison of algebraic and semi-topological K-theory with finite coefficients

Let TT be a dg-category over C\mathbb{C} and let n>0n>0 be an integer. Write K(T)/n\mathbf{K}(T)/n and Kst(T)/n\mathbf{K}^{\mathrm{st}}(T)/n for the reductions modulo nn of the algebraic and semi-topological K-theory spectra. Finite-coefficient comparison conjecture. The map

K(T)/nKst(T)/n\mathbf{K}(T)/n\longrightarrow \mathbf{K}^{\mathrm{st}}(T)/n

is an equivalence. The conjecture is motivated by Thomason's comparison theorem and Friedlander–Walker's analogous result, but the source explicitly allows arbitrary dg-categories and gives no resolution status.

Sources & referencesView supporting material

Primary source

Anthony Blanc, “Topological K-theory of complex noncommutative spaces”, arXiv:1211.7360 (2015).

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