2023/11/02 by Louis, Robin
#14B20 (Secondary) #14F06 (Primary) #Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2312.09438
Let X be a locally Noetherian scheme with a closed subscheme Z. Let X be the completion of X at Z, considered as a formal scheme. We show that a coherent sheaf on X is equivalently given by a coherent sheaf on X, a coherent sheaf on the complement of Z, and an isomorphism of pullbacks of these sheaves to a certain adic space W. By defining W as an adic space instead of as a Berkovich space we are able to generalize the descent result of Ben-Bassat and Temkin from finite type k-schemes to locally Noetherian schemes.