2024/03/13 by Brav, Christopher, Konovalov, Grigorii · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2403.08472
In this paper, we apply Clausen-Scholze's theory of solid modules to the existence of adelic decompositions for schemes of finite type over ℤ. Specifically, we use the six-functor formalism for solid modules to define the skeletal filtration of a scheme, and then we show that decomposing a quasi-coherent sheaf with respect to this filtration gives rise to a new construction of the Beilinson-Parshin adelic resolution. As an application of the adelic decomposition combined with some nice completeness properties of the solid tensor product, we prove a version of adelic descent for solid quasi-coherent sheaves.