Abstract:In this paper, we develop motivic derived algebraic geometry, an enhancement of derived algebraic geometry adapted to the $\mathbb{A}^1$-homotopy theory of Morel and Voevodsky. We construct motivic model categories by imposing descent for a Grothendieck topology and invariance with respect to an interval object, and use them to formulate motivic versions of $\infty$-categories, $\infty$-topoi, and classifying $\infty$-topoi. We then define motivic spectral schemes and motivic spectral Deligne--Mumford stacks in terms of structured motivic $\infty$-topoi. The main result establishes the existence of a motivic stackification functor: a geometric morphism between compatible motivic classifying \(\infty\)-topoi induces a pullback functor on structured motivic topoi, and this functor admits a left adjoint relative to the underlying motivic $\infty$-topos.
From: Yuki Kato [view email]
[v1]
Wed, 8 Mar 2017 14:31:27 UTC (19 KB)
[v2]
Thu, 9 Mar 2017 05:34:07 UTC (19 KB)
[v3]
Thu, 29 Mar 2018 07:46:47 UTC (44 KB)
[v4]
Sun, 31 May 2026 14:28:52 UTC (134 KB)
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