2005/10/20 by Daniel Caro, Caro, Daniel
Computer Science · Mathematics · #14F10 #14F30 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #Polynomial and algebraic computation #Rings, Modules, and Algebras #math.AG #msc:14F10 #msc:14F30
paper · pdf · doi:10.48550/arxiv.math/0510422
62 pages
arxiv created 2005/10/20 · openalex publication_date 2005/10/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let V be a mixed characteristic complete discrete valuation ring, P a separated smooth formal scheme over V, P its special fiber, X a smooth closed subscheme of P, T a divisor in P such that TX = T ∩ X is a divisor in X and \smash\D^†P(\hdag T) the weak completion of the sheaf of differential operators on P with overconvergent singularities along T. We construct a fully faithful functor denoted by \spX \hookrightarrow P,T,+ from the category of isocrystal on X ∖ TX overconvergent along TX into the category of coherent \smash\D^†P(\hdag T) ⊗_ℤ ℚ -modules with support in X. Next, we prove the commutation of \spX \hookrightarrow P,T,+ with (extraordinary) inverse images and dual functors. These properties are compatible with Frobenius.