Results 1  10
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14
Finiteness of rigid cohomology with coefficients
, 2005
"... We prove that for any field k of characteristic p> 0, any separated scheme X of finite type over k, and any overconvergent Fisocrystal E over X, the rigid cohomology Hi rig (X, E) and rigid cohomology with compact supports Hi c,rig (X, E) are finite dimensional vector spaces over an appropriate pa ..."
Abstract

Cited by 16 (11 self)
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We prove that for any field k of characteristic p> 0, any separated scheme X of finite type over k, and any overconvergent Fisocrystal E over X, the rigid cohomology Hi rig (X, E) and rigid cohomology with compact supports Hi c,rig (X, E) are finite dimensional vector spaces over an appropriate padic field. We also establish Poincaré duality and the Künneth formula with coefficients. The arguments use a pushforward construction in relative dimension 1, based on a relative version of Crew’s conjecture on the quasiunipotence of certain padic differential equations.
Local monodromy for padic differential equations: an overview
, 2005
"... This primarily expository article collects together some facts from the literature about the monodromy of differential equations on a padic (rigid analytic) annulus. These include Matsuda’s classification of quasiunipotent ∇modules, the ChristolMebkhout construction of the ramification filtratio ..."
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Cited by 15 (9 self)
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This primarily expository article collects together some facts from the literature about the monodromy of differential equations on a padic (rigid analytic) annulus. These include Matsuda’s classification of quasiunipotent ∇modules, the ChristolMebkhout construction of the ramification filtration, and the ChristolDwork Frobenius antecedent theorem; we also give a formulation of the padic local monodromy theorem.
Slope filtrations revisited
 Doc. Math
"... We give a “second generation ” exposition of the slope filtration theorem for modules with Frobenius action over the Robba ring, providing a number of simplifications in the arguments. Some of these are inspired by parallel work of Hartl and Pink, which points out some analogies with the formalism o ..."
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Cited by 11 (4 self)
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We give a “second generation ” exposition of the slope filtration theorem for modules with Frobenius action over the Robba ring, providing a number of simplifications in the arguments. Some of these are inspired by parallel work of Hartl and Pink, which points out some analogies with the formalism of stable vector bundles.
The padic local monodromy theorem for fake annuli
 Rend. Sem. Mat. Padova
"... We establish a generalization of the padic local monodromy theorem (of André, Mebkhout, and the author) in which differential equations on rigid analytic annuli are replaced by differential equations on socalled “fake annuli”. The latter correspond loosely to completions of a Laurent polynomial ri ..."
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Cited by 8 (8 self)
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We establish a generalization of the padic local monodromy theorem (of André, Mebkhout, and the author) in which differential equations on rigid analytic annuli are replaced by differential equations on socalled “fake annuli”. The latter correspond loosely to completions of a Laurent polynomial ring with respect to a monomial valuation. The result represents a step towards a higherdimensional version of the padic local monodromy theorem (the “problem of semistable reduction”); it can also be viewed as a novel presentation of the original padic local monodromy theorem.
Good formal structures for flat meromorphic connections, II: Higherdimensional varieties
, 2009
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Differential modules on padic polyannuli
, 2008
"... We consider the variational of some numerical invariants, measuring convergence of local horizontal sections, associated to differential modules on polyannuli over a nonarchimedean field. This extends prior work in the onedimensional case of Christol, Dwork, Robba, Young, et al. Contents 1 Differen ..."
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Cited by 5 (5 self)
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We consider the variational of some numerical invariants, measuring convergence of local horizontal sections, associated to differential modules on polyannuli over a nonarchimedean field. This extends prior work in the onedimensional case of Christol, Dwork, Robba, Young, et al. Contents 1 Differential modules over a field 3 1.1 Setup........................................ 3 1.2 Differential fields and differential modules................... 5 1.3 Newton polygons................................. 8
RELATIVE LOG CONVERGENT COHOMOLOGY AND RELATIVE RIGID COHOMOLOGY I
, 2007
"... In this paper, we develop the theory of relative log convergent cohomology. We prove the coherence of relative log convergent cohomology in certain case by using the comparison theorem between relative log convergent cohomlogy and relative log crystalline cohomology, and we relates relative log con ..."
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Cited by 3 (2 self)
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In this paper, we develop the theory of relative log convergent cohomology. We prove the coherence of relative log convergent cohomology in certain case by using the comparison theorem between relative log convergent cohomlogy and relative log crystalline cohomology, and we relates relative log convergent cohomology to relative rigid cohomology to show the validity of Berthelot’s conjecture on the coherence and the overconvergence of relative rigid cohomology for proper smooth families when they admit
III: Local semistable reduction at monomial valuations
, 2007
"... Semistable reduction for overconvergent Fisocrystals, ..."
II: A valuationtheoretic approach
, 2006
"... Semistable reduction for overconvergent Fisocrystals, ..."