research-article

Sums of Betti Numbers in Arbitrary Characteristic

Author:

Nicholas M. KatzAuthors Info & Claims

Finite Fields and Their Applications, Volume 7, Issue 1

Pages 29 - 44

https://doi.org/10.1006/ffta.2000.0303

Published: 01 January 2001 Publication History

Abstract

No abstract available.

References

[1]

A. Adolphson, S. Sperber, On the degree of the L-function associated with an exponential sum, Compositio Math., 68 (1988) 125-159.

Google Scholar

[2]

P. Berthelot, Altérations de variétés algébriques (d'après A. J. de Jong), Exposé 815, Séminaire Bourbaki 1995/96, Astérisque, 241 (1997) 273-311.

Google Scholar

[3]

E. Bombieri, On exponential sums in finite fields, II, Invent. Math., 47 (1978) 29-39.

Crossref

Google Scholar

[4]

A.J. de Jong, Smoothness, semi-stability, and alterations, Inst. Montes Études Sci. Publ. Math., 83 (1996) 51-93.

Crossref

Google Scholar

[5]

P. Deligne, Theoremes de Finitude en Cohomologique ¿¿adique, Springer-Verlag, New York, 1977.

Google Scholar

[6]

P. Deligne, La conjecture de Weil, II, Inst. Montes Études Sci. Publ. Math., 52 (1981) 313-428.

Google Scholar

[7]

B. Dwork, On the rationality of the zeta function of an algebraic variety, Amer. J. Math., 82 (1960) 631-648.

Crossref

Google Scholar

[8]

N. Katz, Affine cohomological transforms, perversity, and monodromy, J. Amer. Math. Soc., 6 (1993) 149-222.

Crossref

Google Scholar

[9]

N. Katz, Estimates for “singular” exponential sums, Internat. Math. Res. Notices, 16 (1999) 875-899.

Crossref

Google Scholar

[10]

G. Laumon, Comparaison de caractéristiques d'Euler¿Poincaré en cohomologie Ql-adique, C.R. Acad. Sci. Paris Sér. I. Math., 292 (1981) 209-212.

Google Scholar

[11]

J. Milnor, On the Betti numbers of real varieties, Proc. Amer. Math. Soc., 15 (1964) 275-280.

Crossref

Google Scholar

[12]

O.A. Oleinik, Estimates of the Betti numbers of real algebraic hypersurfaces (Russian), Mat. Sb. N.S., 28 (1951) 635-640.

Google Scholar

[13]

R. Thom, Sur l'homologie des variétés algébriques réelles, Princeton Univ. Press, Princeton, 1965.

Google Scholar

Cited By

View all

Basu SRizzie A(2018)Multi-degree Bounds on the Betti Numbers of Real Varieties and Semi-algebraic Sets and ApplicationsDiscrete & Computational Geometry10.1007/s00454-017-9944-159:3(553-620)Online publication date: 1-Apr-2018
https://dl.acm.org/doi/10.1007/s00454-017-9944-1
Basu S(2012)A Complex Analogue of Toda's TheoremFoundations of Computational Mathematics10.5555/3115491.311587412:3(327-362)Online publication date: 1-Jun-2012
https://dl.acm.org/doi/10.5555/3115491.3115874
Katz N(2004)Notes on G2, determinants, and equidistributionFinite Fields and Their Applications10.1016/j.ffa.2003.11.00210:2(221-269)Online publication date: 1-Apr-2004
https://dl.acm.org/doi/10.1016/j.ffa.2003.11.002

Recommendations

Characteristic-independence of Betti numbers of graph ideals

In this paper, we study the Betti numbers of Stanley-Reisner ideals generated in degree 2. We show that the first 6 Betti numbers do not depend on the characteristic of the ground field. We also show that, if the number of variables n is at most 10, all ...
Empty Simplices of Polytopes and Graded Betti Numbers

The conjecture of Kalai, Kleinschmidt, and Lee on the number of empty simplices of a simplicial polytope is established by relating it to the first graded Betti numbers of the polytope and applying a result of Migliore and the author. This approach ...
Topological obstructions for vertex numbers of Minkowski sums

We show that for polytopes P"1,P"2,...,P"r@?R^d, each having n"i>=d+1 vertices, the Minkowski sum P"1+P"2+...+P"r cannot achieve the maximum of @?"in"i vertices if r>=d. This complements a recent result of Fukuda and Weibel (2006), who show that this is ...

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

cover image Finite Fields and Their Applications

Finite Fields and Their Applications Volume 7, Issue 1

January, 2001

252 pages

ISSN:1071-5797

Issue’s Table of Contents

Publisher

Elsevier Science Publishers B. V.

Netherlands

Publication History

Published: 01 January 2001

Qualifiers

Research-article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

3
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 18 Dec 2024

Other Metrics

View Author Metrics

Citations

Cited By

View all

Basu SRizzie A(2018)Multi-degree Bounds on the Betti Numbers of Real Varieties and Semi-algebraic Sets and ApplicationsDiscrete & Computational Geometry10.1007/s00454-017-9944-159:3(553-620)Online publication date: 1-Apr-2018
https://dl.acm.org/doi/10.1007/s00454-017-9944-1
Basu S(2012)A Complex Analogue of Toda's TheoremFoundations of Computational Mathematics10.5555/3115491.311587412:3(327-362)Online publication date: 1-Jun-2012
https://dl.acm.org/doi/10.5555/3115491.3115874
Katz N(2004)Notes on G2, determinants, and equidistributionFinite Fields and Their Applications10.1016/j.ffa.2003.11.00210:2(221-269)Online publication date: 1-Apr-2004
https://dl.acm.org/doi/10.1016/j.ffa.2003.11.002

Abstract

References

Cited By

Recommendations

Characteristic-independence of Betti numbers of graph ideals

Empty Simplices of Polytopes and Graded Betti Numbers

Topological obstructions for vertex numbers of Minkowski sums

Comments

Information

Published In

Publisher

Publication History

Qualifiers

Contributors

Other Metrics

Bibliometrics

Article Metrics

Other Metrics

Citations

Cited By

View options

Figures

Other

Share

Share this Publication link

Share on social media

Affiliations