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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

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Affine cohomological transforms, perversity, and monodromy
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by Nicholas M. Katz
J. Amer. Math. Soc. 6 (1993), 149-222
  • A. A. Beĭlinson, J. Bernstein, and P. Deligne, Faisceaux pervers, Analysis and topology on singular spaces, I (Luminy, 1981) Astérisque, vol. 100, Soc. Math. France, Paris, 1982, pp. 5–171 (French). MR 751966
  • Jean-Luc Brylinski, Transformations canoniques, dualité projective, théorie de Lefschetz, transformations de Fourier et sommes trigonométriques, Astérisque 140-141 (1986), 3–134, 251 (French, with English summary). Géométrie et analyse microlocales. MR 864073
  • H. Davenport and D. J. Lewis, Notes on congruences. I, Quart. J. Math. Oxford Ser. (2) 14 (1963), 51–60. MR 146131, DOI 10.1093/qmath/14.1.51
  • Pierre Deligne, La conjecture de Weil. II, Inst. Hautes Études Sci. Publ. Math. 52 (1980), 137–252 (French). MR 601520
  • Bernard Dwork, Generalized hypergeometric functions, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1990. Oxford Science Publications. MR 1085482
  • I. M. Gel′fand, M. M. Kapranov, and A. V. Zelevinsky, Generalized Euler integrals and $A$-hypergeometric functions, Adv. Math. 84 (1990), no. 2, 255–271. MR 1080980, DOI 10.1016/0001-8708(90)90048-R
  • Nicholas M. Katz, Exponential sums and differential equations, Annals of Mathematics Studies, vol. 124, Princeton University Press, Princeton, NJ, 1990. MR 1081536, DOI 10.1515/9781400882434
  • Nicholas M. Katz, Monodromy of families of curves: applications of some results of Davenport-Lewis, Seminar on Number Theory, Paris 1979–80, Progr. Math., vol. 12, Birkhäuser, Boston, Mass., 1981, pp. 171–195. MR 633896
  • Nicholas M. Katz, On the monodromy groups attached to certain families of exponential sums, Duke Math. J. 54 (1987), no. 1, 41–56. MR 885774, DOI 10.1215/S0012-7094-87-05404-4
  • Nicholas M. Katz, Perversity and exponential sums, Algebraic number theory, Adv. Stud. Pure Math., vol. 17, Academic Press, Boston, MA, 1989, pp. 209–259. MR 1097616, DOI 10.2969/aspm/01710209
  • —, Perversity and exponential sums. II: Estimates for and inequalities among $A$-numbers, Proceedings of the Barsotti Memorial Conference (Padua, 1991), to appear
  • Nicholas M. Katz and Gérard Laumon, Transformation de Fourier et majoration de sommes exponentielles, Inst. Hautes Études Sci. Publ. Math. 62 (1985), 361–418 (French). MR 823177
  • G. Laumon, Semi-continuité du conducteur de Swan (d’après P. Deligne), The Euler-Poincaré characteristic (French), Astérisque, vol. 82, Soc. Math. France, Paris, 1981, pp. 173–219 (French). MR 629128
  • Howard H. Mitchell, Determination of All Primitive Collineation Groups in More than Four Variables which Contain Homologies, Amer. J. Math. 36 (1914), no. 1, 1–12. MR 1506202, DOI 10.2307/2370513
  • A. Grothendieck, et al, Séminaire de Géométrie Algébrique du Bois-Marie, SGA 1, SGA 4 Parts I, II, and III, SGA $4\frac {1}{2}$, SGA 5, SGA 7 Parts I and II, Lecture Notes in Math., vols. 224, 269-270-305, 569, 589, 288-340, Springer, New York, 1971 to 1977.
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Bibliographic Information
  • © Copyright 1993 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 6 (1993), 149-222
  • MSC: Primary 14F20; Secondary 14F32, 14G15
  • DOI:
  • MathSciNet review: 1161307