On the zeta function of a complete intersection

Alan Adolphson; Steven Sperber

Annales scientifiques de l'École Normale Supérieure (1996)

  • Volume: 29, Issue: 3, page 287-328
  • ISSN: 0012-9593

How to cite

top

Adolphson, Alan, and Sperber, Steven. "On the zeta function of a complete intersection." Annales scientifiques de l'École Normale Supérieure 29.3 (1996): 287-328. <http://eudml.org/doc/82410>.

@article{Adolphson1996,
author = {Adolphson, Alan, Sperber, Steven},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {-adic Dwork cohomology; Katz conjecture; exponential modules; twisted de Rham theory; zeta function of the complete intersection; Weil conjectures; characteristic polynomial; Newton polygon; Hodge polygon; hypersurfaces; middle-dimensional cohomology},
language = {eng},
number = {3},
pages = {287-328},
publisher = {Elsevier},
title = {On the zeta function of a complete intersection},
url = {http://eudml.org/doc/82410},
volume = {29},
year = {1996},
}

TY - JOUR
AU - Adolphson, Alan
AU - Sperber, Steven
TI - On the zeta function of a complete intersection
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1996
PB - Elsevier
VL - 29
IS - 3
SP - 287
EP - 328
LA - eng
KW - -adic Dwork cohomology; Katz conjecture; exponential modules; twisted de Rham theory; zeta function of the complete intersection; Weil conjectures; characteristic polynomial; Newton polygon; Hodge polygon; hypersurfaces; middle-dimensional cohomology
UR - http://eudml.org/doc/82410
ER -

References

top
  1. [1] A. ADOLPHSON and S. SPERBER, Exponential sums and Newton polyhedra : Cohomology and estimates (Ann. of Math., Vol. 130, 1989, pp. 367-406). Zbl0723.14017MR91e:11094
  2. [2] A. ADOLPHSON and S. SPERBER, Twisted exponential sums and Newton polyhedra (J. reine und angew. Math., Vol. 443, 1993, pp. 151-177). Zbl0853.11067MR95f:14037
  3. [3] A. ADOLPHSON and S. SPERBER, On the degree of the zeta function of a complete intersection, preprint. Zbl0946.14010
  4. [4] J. BARSHAY, On the zeta function of biprojective complete intersections (Trans. A.M.S., Vol. 135, 1969, pp. 447-458). Zbl0174.24302MR38 #1095
  5. [5] V. V. BATYREV, Variations of the mixed Hodge structure of affine hypersurfaces in algebraic tori (Duke Math. J., Vol. 69, 1993, pp. 349-409). Zbl0812.14035MR94m:14067
  6. [6] V. I. DANILOV and A. G. KHOVANSKII, Newton polyhedra and an algorithm for computing Hodge-Deligne numbers (Math. USSR Izvestiya, (2), Vol. 29, 1987, pp. 279-298 (English translation)). Zbl0669.14012
  7. [7] P. DELIGNE, Théorie de Hodge, II (Publ. Math. I.H.E.S., Vol. 40, 1971, pp. 5-57). Zbl0219.14007MR58 #16653a
  8. [8] P. DELIGNE, Théorie de Hodge, III (Publ. Math. I.H.E.S., Vol. 44, 1974, pp. 5-77). Zbl0237.14003MR58 #16653b
  9. [9] B. DWORK, On the zeta function of a hypersurface (Publ. Math. I.H.E.S., Vol. 12, 1962, pp. 5-68). Zbl0173.48601MR28 #3039
  10. [10] B. DWORK, On the zeta function of a hypersurface, II (Ann. of Math., Vol. 80, 1964, pp. 227-299). Zbl0173.48601MR32 #5654
  11. [11] K. IRELAND, On the zeta function of an algebraic variety (Amer. J. Math., Vol. 89, 1967, pp. 643-660). Zbl0197.47201MR36 #1447
  12. [12] A. G. KHOVANSKII, Newton polyhedra and toroidal varieties (Func. Anal. Appl., Vol. 11, 1977, pp. 289-296 (English translation)). Zbl0445.14019MR57 #16291
  13. [13] A. G. KOUCHNIRENKO, Polyèdres de Newton et nombres de Milnor (Invent. Math., Vol. 32, 1976, pp. 1-31). Zbl0328.32007MR54 #7454
  14. [14] B. MAZUR, Frobenius and the Hodge filtration (Bull. A.M.S., Vol. 78, 1972, pp. 653-667). Zbl0258.14006MR48 #8507
  15. [15] P. MONSKY, p-Adic Analysis and Zeta Functions, Lectures in Mathematics, Kyoto University, Tokyo, Kinokuniya Bookstore. Zbl0256.14009
  16. [16] J.-P. SERRE, Endomorphismes complètement continus des espaces de Banach p-adiques (Publ. Math. I.H.E.S., Vol. 12, 1962, pp. 69-85). Zbl0104.33601MR26 #1733
  17. [17] E. SPANIER, Algebraic Topology, McGraw-Hill, New York, 1966. Zbl0145.43303MR35 #1007

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.