Kloosterman sums and monodromy of a p -adic hypergeometric equation

Richard Crew

Compositio Mathematica (1994)

  • Volume: 91, Issue: 1, page 1-36
  • ISSN: 0010-437X

How to cite

top

Crew, Richard. "Kloosterman sums and monodromy of a $p$-adic hypergeometric equation." Compositio Mathematica 91.1 (1994): 1-36. <http://eudml.org/doc/90279>.

@article{Crew1994,
author = {Crew, Richard},
journal = {Compositio Mathematica},
keywords = {overconvergent crystals; characteristic ; differential Galois-groups; Kloosterman sums; Frobenius-elements},
language = {eng},
number = {1},
pages = {1-36},
publisher = {Kluwer Academic Publishers},
title = {Kloosterman sums and monodromy of a $p$-adic hypergeometric equation},
url = {http://eudml.org/doc/90279},
volume = {91},
year = {1994},
}

TY - JOUR
AU - Crew, Richard
TI - Kloosterman sums and monodromy of a $p$-adic hypergeometric equation
JO - Compositio Mathematica
PY - 1994
PB - Kluwer Academic Publishers
VL - 91
IS - 1
SP - 1
EP - 36
LA - eng
KW - overconvergent crystals; characteristic ; differential Galois-groups; Kloosterman sums; Frobenius-elements
UR - http://eudml.org/doc/90279
ER -

References

top
  1. [1] P. Berthelot, Géometrie rigide et cohomologie des variétés algébriques de caracteristique p, Journés d'analyse p-adique (Luminy1982), Mémoire de la S.M.F. No. 23, suppl. au Bull. S.M.F.114 (1986) fasc.2, 7-32. Zbl0606.14017MR865810
  2. [2] P. Berthelot, Cohomologie rigide et théorie de Dwork: le cas des sommes exponentielles, in Astérisque119-120 (1984) 17-49. Zbl0577.14013MR773087
  3. [3] P. Berthelot, Cohomologie rigide et cohomologie rigide á support propre, to appear in Astérisque. Zbl0515.14015MR773087
  4. [4] A. Borel, Linear algebraic groups, 2nd ed., Springer-Verlag (1991). Zbl0726.20030MR1102012
  5. [5] S. Bosch, B. Dwork, and Ph. Robba, A rigid analytic version of M. Artin's theorem on analytic equations, Math. Ann.255 (1981) 395-404. Zbl0462.14002MR615859
  6. [6] R. Crew, F-isocrystals and p-adic representations, in Algebraic Geometry-Bowdoin 1985, Proc. Symp. Pure Math.46(2) (1987) 111-138. Zbl0639.14011MR927977
  7. [7] R. Crew, F-isocrystals and their monodromy groups, Ann. Sc. Ec. Norm. Sup.4e sér. 25 (1992) 429-464. Zbl0783.14008MR1186910
  8. [8] P. Deligne, La conjecture de Weil II, Publ. Math. IHES52 (1980) 137-352. Zbl0456.14014MR601520
  9. [9] P. Deligne and J. Milne, Tannakian Categories, in Lecture Notes in Math. 900, Springer-Verlag (1982). Zbl0477.14004
  10. [10] B. Dwork, Bessel functions as p-adic functions of the argument, Duke Math. J.41 (1974) 711-738. Zbl0302.14008MR387281
  11. [11] S. Helgason, Differential geometry and symmetric spaces, Academic Press (1962). Zbl0111.18101MR145455
  12. [12] N. Katz, Travauxs de Dwork, Séminaire Bourbaki1971 -2, exposé 409, in Lecture Notes in Math. 317, Springer-Verlag (1973), pp. 167-200. Zbl0259.14007MR498577
  13. [13] N. Katz, p-adic properties of modular schemes and modular forms, in Lecture Notes in Math. 350, Springer-Verlag (1973), 69-190. Zbl0271.10033MR447119
  14. [14] N. Katz, Slope filtration of F-crystals, in Journées de géométrie algébrique de Rennes I, Astérisque63 (1979) 113-163. Zbl0426.14007MR563463
  15. [15] N. Katz, On the calculation of some differential galois groups, Inv. Math.87 (1987) 13-61. Zbl0609.12025MR862711
  16. [16] N. Katz, Gauss sums, Kloosterman sums, and monodromy groups, Annals of Math. Studies116, Princeton Univ. Press (1988). Zbl0675.14004MR955052
  17. [17] N. Katz, Exponential sums and differential equations, Annals of Math. Studies124, Princeton Univ. Press (1990). Zbl0731.14008MR1081536
  18. [18] M. Larsen and R. Pink, On l-independence of algebraic monodromy groups in compatible systems of representations, preprint. Zbl0778.11036
  19. [19] A. Ogus, F-isocrystals and De Rham cohomology II - Convergent isocrystals, Duke J. Math.51 (1984) 765-850. Zbl0584.14008MR771383
  20. [20] N. Saavedra R., Categories Tannakiennes, Lecture Notes in Math. 265, Springer-Verlag (1972). Zbl0241.14008MR338002
  21. [21] J.-P. Serre, Abelian l-adic representations and elliptic curves, W. A. Benjamin (1968). Zbl0186.25701MR263823
  22. [22] S. Sperber, p-adic hypergeometric functions and their cohomology, Duke Math. J.44 (1977) 535-589. Zbl0408.12025MR476750
  23. [23] S. Sperber, Congruence properties of the hyperkloosterman sum, Com. Math.40 (1980) 3-33. Zbl0444.12014MR558257
  24. [24] S. Sperber, Newton polygons for general hyperkloosterman sums, in Cohomologie p-adique, Astérisque119-120 (1984) 267-330. Zbl0582.14005MR773095
  25. [LIE] N. Bourbaki, Groupes et algèbres de Lie, Masson, Paris (1982). Zbl0505.22006
  26. [SGA 41/2] P. Deligne et al., Cohomologie étale, Lecture Notes in Math. 569, Springer-Verlag (1977). Zbl0345.00010MR463174

NotesEmbed ?

top

You must be logged in to post comments.