Abstract:
The absolute purity conjecture, introduced by Grothendieck, plays an important role in the cohomological studies of schemes. While this conjecture has been solved by Gabber for étale cohomology, its counterpart in motivic homotopy theory remains an interesting open question. In this talk we show that the rational motivic sphere spectrum satisfies absolute purity, and discuss some applications. This is a joint work with F. Déglise, J. Fasel and A. Khan.
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