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Dipankar Maity

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Preprint Aug 2026

$\mathbb{P}^1$ Homotopy Theory of Schemes

We study the $\mathbb{P}^1$-local motivic homotopy theory under the Nisnevich topology on $Sm_S$. We show that although the homotopy category $\mathcal{H}^{\mathbb{P}^1}(-)$ admits standard schematic functorialities, it fails six-functor gluing, thereby obstructing a full six-functor formalism. On the unstable side, we...

Dipankar Maity · 0 citations