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D-modules arithmétiques associés aux isocristaux surconvergents. Cas lisse | | Daniel Caro
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20 Oct 2005 | | Abstract: | Let $mathcal{V}$ be a mixed characteristic complete discrete valuation ring, $mathcal{P}$ a separated smooth formal scheme over $mathcal{V}$, $P$ its special fiber, $X$ a smooth closed subscheme of $P$, $T$ a divisor in $P$ such that $T_X = T cap X$ is a divisor in $X$ and $smash{D}^dag _{mathcal{P}}(hdag T)$ the weak completion of the sheaf of differential operators on $mathcal{P}$ with overconvergent singularities along $T$. We construct a fully faithful functor denoted by $ sp_{X hookrightarrow mathcal{P},T,+}$ from the category of isocrystal on $X setminus T_X$ overconvergent along $T_X$ into the category of coherent $smash{D}^dag _{mathcal{P}}(hdag T) otimes_mathbb{Z} mathbb{Q} $-modules with support in $X$. Next, we prove the commutation of $ sp_{X hookrightarrow mathcal{P},T,+}$ with (extraordinary) inverse images and dual functors. These properties are compatible with Frobenius. | | Source: | arXiv, math.AG/0510422 | | Services: | Forum | Review | PDF | Favorites | |
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