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arxiv: 2112.14723 · v1 · pith:I3HIVUCVnew · submitted 2021-12-29 · 🧮 math.KT · math.AT

On the K-theory of regular coconnective rings

classification 🧮 math.KT math.AT
keywords k-theorycategoriescoconnectivegeneralresultagreesalgebraicapplications
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We show that for a coconnective ring spectrum satisfying regularity and flatness assumptions, its algebraic K-theory agrees with that of its $\pi_0$. We prove this as a consequence of a more general devissage result for stable infinity categories. Applications of our result include giving general conditions under which K-theory preserves pushouts, generalizations of $\mathbb{A}^n$-invariance of K-theory, and an understanding of the K-theory of categories of unipotent local systems.

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    Introduces arithmetic C(S^1,R)-modules whose K_0 yields Euler characteristics for perfect etale Z_l-sheaves and prismatic F-gauges without Tate semi-simplicity, removing the assumption from Milne's cohomological zeta-...