2004
DOI: 10.1515/crll.2004.028
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Image directe supérieure et unipotence

Abstract: Let X be a proper smooth curve over a perfect field of characteristic p > 0 and U an open dense subscheme of X. We prove that convergent F-isocrystals on U are overconvergent under the condition that they are overconvergent at each point in X \ U. Using this criterion, we show that the higher direct images R i f crys * O V by a proper smooth morphism of schemes f : V → U are overconvergent.

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Cited by 91 publications
(297 citation statements)
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“…Matsuda et al 2004;Saito et al 2006;Nilsson et al 2006;Smith & Jarvis 2007). Lyα blobs are found mostly at z ≃ 2 − 3, and have angular extents of ≃ 5 − 16 arcsec with total Lyα luminosities ranging from ≃ 6 × 10 42 to 10 44 erg s −1 (Matsuda et al 2004). The most prominent Lyα nebulae known to date are blobs 1 and 2 found by Steidel et al (2000), which extend over 100 kpc with L(Lyα) ≃ 10 44 erg s −1 .…”
Section: Introductionmentioning
confidence: 91%
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“…Matsuda et al 2004;Saito et al 2006;Nilsson et al 2006;Smith & Jarvis 2007). Lyα blobs are found mostly at z ≃ 2 − 3, and have angular extents of ≃ 5 − 16 arcsec with total Lyα luminosities ranging from ≃ 6 × 10 42 to 10 44 erg s −1 (Matsuda et al 2004). The most prominent Lyα nebulae known to date are blobs 1 and 2 found by Steidel et al (2000), which extend over 100 kpc with L(Lyα) ≃ 10 44 erg s −1 .…”
Section: Introductionmentioning
confidence: 91%
“…We carry out the simulations in the same manner as Saito et al (2006), but with an improved random noise whose amplitude exactly matches to those of real N B921 image. Figure 7 presents the simulated N B921 images, together with the original narrow-band images of Matsuda et al (2004). The simulated image of blob 1 indicates that our observations would miss ≃ 95% of blob 1's L(Lyα), and that no diffuse Lyα nebula could be identified.…”
Section: Comparisons With Lyα Blobs At Z ∼mentioning
confidence: 99%
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“…Since S is an affine curve, Berthelot's conjecture discussed in Remark 1.2 is known to have an affirmative answer by S. Matsuda and F. Trihan [34]: a unique overconvergent extension R i f * O † X/K of R i f * O X/K exists for each i ≥ 0. It is then not unreasonable to claim that there "obviously" exists a Leray spectral sequence in rigid cohomology, namely…”
Section: Crystalline Théorème De La Partie Fixementioning
confidence: 99%