2012/07/03 by Daniel Caro, Caro, Daniel
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1207.0710
openalex publication_date 2012/07/03 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
Let \V be a complete discrete valuation ring of unequal\ncharacteristic with perfect residue field, \P be a smooth,\nquasi-compact, separated formal scheme over \V, \Z be a\nstrict normal crossing divisor of \P and \P^ sharp :=\n(\P, \Z) the induced smooth formal log-scheme over\n\V. In Berthelot's theory of arithmetic \D-modules, we\nwork with the inductive system of sheaves of rings\n smash\\D\P ^ sharp ( bullet) :=\n( smash\\D\P^ sharp (m))m\∈ \ℕ,\nwhere smash\\D\P sharp (m) is the p-adic\ncompletion of the ring of differential operators of level m over\n\P sharp. Moreover, he introduced the sheaf \D\n^\†\P\n sharp,\ℚ:= underset undersetm longrightarrow\lim ,\n smash\\D\P (m) \⊗\ℤ\ℚ\nof differential operators over \P of finite level. In this paper, we\ndefine the notion of overcoherence for complexes of\n smash\\D\P sharp ( bullet) -modules and\ncheck that this notion is compatible to that of overcoherence for complexes of\n\D ^\†\P,\ℚ-modules.\n