Motivic Landweber Exactness

Model topoi and motivic homotopy theory

Given a small simplicial category $\C$ whose underlying ordinary category is equipped with a Grothendieck topology $τ$, we construct a model structure on the category of simplicially enriched presheaves on $\C$ where the weak equivalences are the local weak equivalences of the underlying (non-enriched) simplicial presheaves. We show that this model category is a $t$-complete model topos and describe the Grothendieck topology $[τ]$ on the homotopy category of $\C$ that corresponds to this model topos. After we first review a proof showing that the motivic homotopy theory is not a model topos, w…

动机谱的 Atiyah 对偶

Atiyah duality for motivic spectra

本文证明任意导出概形上非 𝔸¹-不变动机谱 ∞-范畴中的 Atiyah 对偶，并据此发展共局部化与动机 Landweber 正合函子定理，应用于对数上同调、代数 K-理论运算及有理动机上同调。