2025/03/31 by Cisinski, Denis-Charles
#Algebraic Geometry (math.AG) #FOS: Mathematics #K-Theory and Homology (math.KT) #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2503.24033
We study the process of ℓ-adic completion of motivic sheaves. We observe that, in equal characteristic, when restricted to constructible objets, it is compatible with the six operations. This implies that one can reconstruct ℓ-adic sheaves of geometric origin over a scheme of finite type over a field from ℓ-adic cohomology of smooth schemes. In the case of finite fields, this includes perverse ℓ-adic sheaves of geometric orgin. However, the analogous behaviour fails systematically in mixed characteristic: the reason is that it would imply strong independence of ℓ results that can be proven to be too optimistic.