Slope filtration of quasi-unipotent overconvergent F -isocrystals

Nobuo Tsuzuki

Annales de l'institut Fourier (1998)

  • Volume: 48, Issue: 2, page 379-412
  • ISSN: 0373-0956

Abstract

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We study local properties of quasi-unipotent overconvergent F -isocrystals on a curve over a perfect field of positive characteristic p . For a φ - ∇ -module over the Robba ring ℛ , we define the slope filtration for Frobenius structures. We prove that an overconvergent F -isocrystal is quasi-unipotent if and only if it has the slope filtration for Frobenius structures locally at every point on the complement of the curve.

How to cite

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Tsuzuki, Nobuo. "Slope filtration of quasi-unipotent overconvergent $F$-isocrystals." Annales de l'institut Fourier 48.2 (1998): 379-412. <http://eudml.org/doc/75286>.

@article{Tsuzuki1998,
abstract = {We study local properties of quasi-unipotent overconvergent $F$-isocrystals on a curve over a perfect field of positive characteristic $p$. For a $\varphi $-$\nabla $-module over the Robba ring $\{\cal R\}$, we define the slope filtration for Frobenius structures. We prove that an overconvergent $F$-isocrystal is quasi-unipotent if and only if it has the slope filtration for Frobenius structures locally at every point on the complement of the curve.},
author = {Tsuzuki, Nobuo},
journal = {Annales de l'institut Fourier},
keywords = {overconvergent -isocrystals on curves; Frobenius-crystals; Robba ring; unipotent crystals; slope-filtration},
language = {eng},
number = {2},
pages = {379-412},
publisher = {Association des Annales de l'Institut Fourier},
title = {Slope filtration of quasi-unipotent overconvergent $F$-isocrystals},
url = {http://eudml.org/doc/75286},
volume = {48},
year = {1998},
}

TY - JOUR
AU - Tsuzuki, Nobuo
TI - Slope filtration of quasi-unipotent overconvergent $F$-isocrystals
JO - Annales de l'institut Fourier
PY - 1998
PB - Association des Annales de l'Institut Fourier
VL - 48
IS - 2
SP - 379
EP - 412
AB - We study local properties of quasi-unipotent overconvergent $F$-isocrystals on a curve over a perfect field of positive characteristic $p$. For a $\varphi $-$\nabla $-module over the Robba ring ${\cal R}$, we define the slope filtration for Frobenius structures. We prove that an overconvergent $F$-isocrystal is quasi-unipotent if and only if it has the slope filtration for Frobenius structures locally at every point on the complement of the curve.
LA - eng
KW - overconvergent -isocrystals on curves; Frobenius-crystals; Robba ring; unipotent crystals; slope-filtration
UR - http://eudml.org/doc/75286
ER -

References

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