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Abstract
Weibel proved that
p -inverted
K-theory is
𝔸 1 -invariant on
𝔽 p -schemes and K-theory
with
ℤ ∕ p -coefficients
is
𝔸 1 -invariant
on
ℤ [ 1
p ] -schemes.
We extend this result to all finitary localizing invariants of small stable
∞ -categories.
Along the way we study the Frobenius and Verschiebung endofunctors defined by
Tabuada and provide a categorical version of Stienstra’s projection formula.
Keywords
noncommutative motives, localizing invariants,
$\mathbb{A}^1$-invariance, Witt vectors
Mathematical Subject Classification
Primary: 13F35, 14F42, 18F25
Milestones
Received: 7 January 2023
Revised: 19 February 2024
Accepted: 3 March 2024
Published: 25 May 2024
© 2024 The Author(s), under
exclusive license to MSP (Mathematical Sciences
Publishers).