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\mathrm{dMGL}^{a,\rm fin}(A) \simeq \mathrm{dMGL}^{a,\rm fin}(A^\flat). \] This invariant is a finite syntomic, derived, and non-$\mathbb{A}^1$-local version of algebraic cobordism, designed to retain infinitesimal deformation data over mixed characteristic bases. To prove the result, we first establish the corresponding finite non-unital statement and isolate a form of excisive approximation for pointed $\infty$-categories, including non-presentable ones. In the locally finitely presentable case, this agrees with the framework of Heuts. We also define approximation functors along natural transformations and apply them to the comparison between periodic algebraic cobordism and homotopy $K$-theory, obtaining Bott periodicity and Gabber rigidity.
From: Yuki Kato [view email]
[v1]
Fri, 16 May 2025 03:10:15 UTC (21 KB)
[v2]
Fri, 12 Sep 2025 09:10:08 UTC (134 KB)
[v3]
Sun, 31 May 2026 14:20:20 UTC (131 KB)
[v4]
Thu, 18 Jun 2026 09:03:29 UTC (131 KB)
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