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Log-isocristaux surconvergents et holonomie
- Part of
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- Journal:
- Compositio Mathematica / Volume 145 / Issue 6 / November 2009
- Published online by Cambridge University Press:
- 24 September 2009, pp. 1465-1503
- Print publication:
- November 2009
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- Article
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Let 𝒱 be a complete discrete valuation ring of unequal characteristic with perfect residue field. Let
be a separated smooth formal 𝒱-scheme, 𝒵 be a normal crossing divisor of , 
be the induced formal log-scheme over 𝒱 and 
be the canonical morphism. Let X and Z be the special fibers of and 𝒵, T be a divisor of X and ℰ be a log-isocrystal on 
overconvergent along T, that is, a coherent left 
-module, locally projective of finite type over 
. We check the relative duality isomorphism: 
. We prove the isomorphism 
, which implies their holonomicity as 
-modules. We obtain the canonical morphism ρℰ : uT,+(ℰ)→ℰ(†Z). When ℰ is moreover an isocrystal on overconvergent along T, we prove that ρℰ is an isomorphism.
be a separated smooth formal 𝒱-scheme, 𝒵 be a normal crossing divisor of 
be the induced formal log-scheme over 𝒱 and 
be the canonical morphism. Let 
overconvergent along 
-module, locally projective of finite type over 
. We check the relative duality isomorphism: 
. We prove the isomorphism 
, which implies their holonomicity as 
-modules. We obtain the canonical morphism 