Categorical Milnor squares and K-theory of algebraic stacks

We show that for a coconnective ring spectrum satisfying regularity and flatness assumptions, its algebraic K-theory agrees with that of its $$\pi _0$$ π 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 $$\mathbb {A}^n$$ A n -invariance of K-theory, and an understanding of the K-theory of categories of unipotent local systems.

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On the K-theory of regular coconnective rings

Burklund

Levy

2023

Sel. Math. New Ser.

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Generalized cohomology theories for algebraic stacks

Khan,

Ravi

2024

Advances in Mathematics

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𝔸1-invariance of localizing invariants

Sosnilo

2024

Ann. K-Th.

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Categorical Milnor squares and K-theory of algebraic stacks

Cited by 3 publications

References 35 publications

On the K-theory of regular coconnective rings

On the K-theory of regular coconnective rings

Generalized cohomology theories for algebraic stacks

𝔸1-invariance of localizing invariants

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