Deligne's purity conjecture for constructible l-adic sheaves

Let XX be a scheme over Fp\mathbf{F}_p, and let FF be a constructible Ql\mathbf{Q}_l-sheaf on XX. Purity conjecture. Every constructible Ql\mathbf{Q}_l-sheaf on XX is mixed.

This is presented as a striking conjecture in the theory of weights of l-adic sheaves. The supplied text does not state its resolution or provide enough information to determine whether the assertion is intended in a more precise ι\iota-mixed formulation.

Sources & referencesView supporting material

Primary source

Bruno Kahn, “Fonctions zêta et L de variétés et de motifs”, arXiv:1512.09250 (2016).

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