On systems of linear inequalities

Masami Fujimori

Bulletin de la Société Mathématique de France (2003)

  • Volume: 131, Issue: 1, page 41-57
  • ISSN: 0037-9484

Abstract

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We show in detail that the category of general Roth systems or the category of semi-stable systems of linear inequalities of slope zero is a neutral Tannakian category. On the way, we present a new proof of the semi-stability of the tensor product of semi-stable systems. The proof is based on a numerical criterion for a system of linear inequalities to be semi-stable.

How to cite

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Fujimori, Masami. "On systems of linear inequalities." Bulletin de la Société Mathématique de France 131.1 (2003): 41-57. <http://eudml.org/doc/272439>.

@article{Fujimori2003,
abstract = {We show in detail that the category of general Roth systems or the category of semi-stable systems of linear inequalities of slope zero is a neutral Tannakian category. On the way, we present a new proof of the semi-stability of the tensor product of semi-stable systems. The proof is based on a numerical criterion for a system of linear inequalities to be semi-stable.},
author = {Fujimori, Masami},
journal = {Bulletin de la Société Mathématique de France},
keywords = {semi-stability; successive minima; tannakian category; tensor product},
language = {eng},
number = {1},
pages = {41-57},
publisher = {Société mathématique de France},
title = {On systems of linear inequalities},
url = {http://eudml.org/doc/272439},
volume = {131},
year = {2003},
}

TY - JOUR
AU - Fujimori, Masami
TI - On systems of linear inequalities
JO - Bulletin de la Société Mathématique de France
PY - 2003
PB - Société mathématique de France
VL - 131
IS - 1
SP - 41
EP - 57
AB - We show in detail that the category of general Roth systems or the category of semi-stable systems of linear inequalities of slope zero is a neutral Tannakian category. On the way, we present a new proof of the semi-stability of the tensor product of semi-stable systems. The proof is based on a numerical criterion for a system of linear inequalities to be semi-stable.
LA - eng
KW - semi-stability; successive minima; tannakian category; tensor product
UR - http://eudml.org/doc/272439
ER -

References

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  2. [2] P. Deligne & J. Milne – « Tannakian Categories », Hodge Cycles, Motives, and Shimura Varieties (P. Deligne & al., éds.), Lect. Notes in Math., vol. 900, Springer-Verlag, Berlin Heidelberg, 1982, p. 101–228. Zbl0477.14004MR654325
  3. [3] G. Faltings – « Mumford-Stabilität in der algebraischen Geometrie », Proceedings of the International Congress of Mathematicians 1994 (Zürich, Switzerland), Birkhäuser Verlag, 1995, p. 648–655. Zbl0871.14010MR1403965
  4. [4] G. Faltings & G. Wüstholz – « Diophantine approximations on projective spaces », Invent. Math.116 (1994), p. 109–138. Zbl0805.14011MR1253191
  5. [5] R. Ferretti – « Quantitative Diophantine approximations on projective varieties », preprint, http://www.math.ethz.ch/~ferretti, 8 July 1999. 
  6. [6] H. Schlickewei – « Linearformen mit algebraischen Koeffizienten », Manuscripta Math.18 (1976), p. 147–185. Zbl0323.10028MR401665
  7. [7] W. Schmidt – « Linear forms with algebraic coefficients, I », J. Number Theory3 (1971), p. 253–277. Zbl0221.10034MR308061
  8. [8] B. Totaro – « Tensor products of semistables are semistable », Geometry and Analysis on Complex Manifolds, World Scientific Publishing, River Edge, NJ, 1994, p. 242–250. Zbl0873.14016MR1463972
  9. [9] —, « Tensor products in p -adic Hodge theory », Duke Math. J.83 (1996), p. 79–104. Zbl0873.14019MR1388844

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