Compute Distance To:
 Author ID: lyubeznik.gennady Published as: Lyubeznik, Gennady; Lyubeznik, G.
 Documents Indexed: 48 Publications since 1982 1 Contribution as Editor Co-Authors: 16 Co-Authors with 19 Joint Publications 613 Co-Co-Authors
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### Co-Authors

 30 single-authored 8 Zhang, Wenliang 4 Blickle, Manuel 4 Katzman, Mordechai 4 Singh, Anurag K. 3 Bhatt, Bhargav 2 Huneke, Craig L. 2 Smith, Karen E. 1 Àlvarez Montaner, Josep 1 Barile, Margherita 1 Call, Frederick W. 1 Greenlees, John P. C. 1 Luo, Zhi-Quan 1 Razaviyayn, Meisam 1 Walther, Uli 1 Yıldırım, Tuğba 1 Zhang, Yi
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### Serials

 8 Proceedings of the American Mathematical Society 6 Journal of Pure and Applied Algebra 5 Journal of Algebra 3 American Journal of Mathematics 3 Inventiones Mathematicae 2 Advances in Mathematics 2 Mathematische Zeitschrift 1 Communications in Algebra 1 Archiv der Mathematik 1 Bulletin of the London Mathematical Society 1 Compositio Mathematica 1 Journal für die Reine und Angewandte Mathematik 1 Mathematische Annalen 1 Michigan Mathematical Journal 1 Transactions of the American Mathematical Society 1 IEEE Transactions on Signal Processing 1 Bulletin of the American Mathematical Society. New Series 1 Mathematical Research Letters 1 Annals of Mathematics. Second Series 1 Journal of the European Mathematical Society (JEMS) 1 Lecture Notes in Pure and Applied Mathematics
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### Fields

 41 Commutative algebra (13-XX) 20 Algebraic geometry (14-XX) 3 Group theory and generalizations (20-XX) 2 Associative rings and algebras (16-XX) 1 General and overarching topics; collections (00-XX) 1 Combinatorics (05-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Convex and discrete geometry (52-XX) 1 Manifolds and cell complexes (57-XX) 1 Information and communication theory, circuits (94-XX)

### Citations contained in zbMATH Open

42 Publications have been cited 782 times in 497 Documents Cited by Year
Finiteness properties of local cohomology modules (an application of $$D$$- modules to commutative algebra). Zbl 0795.13004
1993
$$F$$-modules: Applications to local cohomology and $$D$$-modules in characteristic $$p>0$$. Zbl 0904.13003
1997
On the vanishing of local cohomology modules. Zbl 0717.13011
Huneke, Craig; Lyubeznik, G.
1990
On the commutation of the test ideal with localization and completion. Zbl 0977.13002
Lyubeznik, Gennady; Smith, Karen E.
2001
Finiteness properties of local cohomology modules for regular local rings of mixed characteristic: The unramified case. Zbl 0981.13008
2000
On the arithmetical rank of monomial ideals. Zbl 0639.13015
1988
Strong and weak F-regularity are equivalent for graded rings. Zbl 0970.13003
Lyubeznik, Gennady; Smith, Karen E.
1999
A new explicit finite free resolution of ideals generated by monomials in an R-sequence. Zbl 0652.13012
1988
On the vanishing of local cohomology in characteristic $$p>0$$. Zbl 1100.13022
2006
A simple proof of Grothendieck’s theorem on the parafactoriality of local rings. Zbl 0813.13017
Call, Frederick; Lyubeznik, Gennady
1994
Generators of $$D$$-modules in positive characteristic. Zbl 1115.13032
Alvarez-Montaner, Josep; Blickle, Manuel; Lyubeznik, Gennady
2005
Absolute integral closure in positive characteristic. Zbl 1109.13003
Huneke, Craig; Lyubeznik, Gennady
2007
A partial survey of local cohomology. Zbl 1061.14005
2002
Finiteness properties of local cohomology modules: A characteristic-free approach. Zbl 0964.13010
2000
On the discreteness and rationality of $$F$$-jumping coefficients. Zbl 1186.13003
Katzman, Mordechai; Lyubeznik, Gennady; Zhang, Wenliang
2009
Local cohomology modules of a smooth $$\mathbb{Z}$$-algebra have finitely many associated primes. Zbl 1318.13025
Bhatt, Bhargav; Blickle, Manuel; Lyubeznik, Gennady; Singh, Anurag K.; Zhang, Wenliang
2014
On some local cohomology invariants of local rings. Zbl 1105.13019
2006
Local cohomology modules supported at determinantal ideals. Zbl 1408.13047
Lyubeznik, Gennady; Singh, Anurag K.; Walther, Uli
2016
The number of defining equations of affine algebraic sets. Zbl 0770.14021
1992
On some local cohomology modules. Zbl 1121.13016
2007
The minimal non-Cohen-Macaulay monomial ideals. Zbl 0655.13020
1988
Set-theoretic complete intersections in characteristic $$p$$. Zbl 1077.14064
Barile, Margherita; Lyubeznik, Gennady
2005
Injective dimension of $$D$$-modules: A characteristic-free approach. Zbl 0989.13010
2000
Rings with a local cohomology theorem and applications to cohomology rings of groups. Zbl 0965.13012
Greenlees, J. P. C.; Lyubeznik, G.
2000
Etale cohomological dimension and the topology of algebraic varieties. Zbl 0811.14014
1993
Some algebraic sets of high local cohomological dimension in projective space. Zbl 0587.14002
1985
A characteristic-free proof of a basic result on $$\mathcal D$$-modules. Zbl 1211.13016
2011
On set-theoretic intersections. Zbl 0575.14041
1984
A survey of problems and results on the number of defining equations. Zbl 0753.14001
1989
On the local cohomology modules $$H^ i_{{\mathfrak a}}(R)$$ for ideals $${\mathfrak a}$$ generated by monomials in an R-sequence. Zbl 0578.13012
1984
An extension of a theorem of Hartshorne. Zbl 1419.13032
Katzman, Mordechai; Lyubeznik, Gennady; Zhang, Wenliang
2016
A property of ideals in polynomial rings. Zbl 0612.13008
1986
On Bernstein-Sato polynomials. Zbl 0878.13018
1997
Stabilization of the cohomology of thickenings. Zbl 1425.13008
Bhatt, Bhargav; Blickle, Manuel; Lyubeznik, Gennady; Singh, Anurag K.; Zhang, Wenliang
2019
A property of the Frobenius map of a polynomial ring. Zbl 1239.13009
Lyubeznik, Gennady; Zhang, Wenliang; Zhang, Yi
2011
A generalization of Lichtenbaum’s theorem on the cohomological dimension of algebraic varieties. Zbl 0724.14010
1991
The number of generators of modules over polynomial rings. Zbl 0667.13006
1988
Minimal resultant systems. Zbl 0856.13004
1995
An upper bound on the number of $$F$$-jumping coefficients of a principal ideal. Zbl 1230.13007
Katzman, Mordechai; Lyubeznik, Gennady; Zhang, Wenliang
2011
The number of equations needed to define an algebraic set. Zbl 0678.14012
1988
Local cohomology and its applications. Selected papers of the international workshop, Guanajuato, Mexico. Zbl 0974.00036
2002
An asymptotic vanishing theorem for the cohomology of thickenings. Zbl 1481.13032
Bhatt, Bhargav; Blickle, Manuel; Lyubeznik, Gennady; Singh, Anurag K.; Zhang, Wenliang
2021
An asymptotic vanishing theorem for the cohomology of thickenings. Zbl 1481.13032
Bhatt, Bhargav; Blickle, Manuel; Lyubeznik, Gennady; Singh, Anurag K.; Zhang, Wenliang
2021
Stabilization of the cohomology of thickenings. Zbl 1425.13008
Bhatt, Bhargav; Blickle, Manuel; Lyubeznik, Gennady; Singh, Anurag K.; Zhang, Wenliang
2019
Local cohomology modules supported at determinantal ideals. Zbl 1408.13047
Lyubeznik, Gennady; Singh, Anurag K.; Walther, Uli
2016
An extension of a theorem of Hartshorne. Zbl 1419.13032
Katzman, Mordechai; Lyubeznik, Gennady; Zhang, Wenliang
2016
Local cohomology modules of a smooth $$\mathbb{Z}$$-algebra have finitely many associated primes. Zbl 1318.13025
Bhatt, Bhargav; Blickle, Manuel; Lyubeznik, Gennady; Singh, Anurag K.; Zhang, Wenliang
2014
A characteristic-free proof of a basic result on $$\mathcal D$$-modules. Zbl 1211.13016
2011
A property of the Frobenius map of a polynomial ring. Zbl 1239.13009
Lyubeznik, Gennady; Zhang, Wenliang; Zhang, Yi
2011
An upper bound on the number of $$F$$-jumping coefficients of a principal ideal. Zbl 1230.13007
Katzman, Mordechai; Lyubeznik, Gennady; Zhang, Wenliang
2011
On the discreteness and rationality of $$F$$-jumping coefficients. Zbl 1186.13003
Katzman, Mordechai; Lyubeznik, Gennady; Zhang, Wenliang
2009
Absolute integral closure in positive characteristic. Zbl 1109.13003
Huneke, Craig; Lyubeznik, Gennady
2007
On some local cohomology modules. Zbl 1121.13016
2007
On the vanishing of local cohomology in characteristic $$p>0$$. Zbl 1100.13022
2006
On some local cohomology invariants of local rings. Zbl 1105.13019
2006
Generators of $$D$$-modules in positive characteristic. Zbl 1115.13032
Alvarez-Montaner, Josep; Blickle, Manuel; Lyubeznik, Gennady
2005
Set-theoretic complete intersections in characteristic $$p$$. Zbl 1077.14064
Barile, Margherita; Lyubeznik, Gennady
2005
A partial survey of local cohomology. Zbl 1061.14005
2002
Local cohomology and its applications. Selected papers of the international workshop, Guanajuato, Mexico. Zbl 0974.00036
2002
On the commutation of the test ideal with localization and completion. Zbl 0977.13002
Lyubeznik, Gennady; Smith, Karen E.
2001
Finiteness properties of local cohomology modules for regular local rings of mixed characteristic: The unramified case. Zbl 0981.13008
2000
Finiteness properties of local cohomology modules: A characteristic-free approach. Zbl 0964.13010
2000
Injective dimension of $$D$$-modules: A characteristic-free approach. Zbl 0989.13010
2000
Rings with a local cohomology theorem and applications to cohomology rings of groups. Zbl 0965.13012
Greenlees, J. P. C.; Lyubeznik, G.
2000
Strong and weak F-regularity are equivalent for graded rings. Zbl 0970.13003
Lyubeznik, Gennady; Smith, Karen E.
1999
$$F$$-modules: Applications to local cohomology and $$D$$-modules in characteristic $$p>0$$. Zbl 0904.13003
1997
On Bernstein-Sato polynomials. Zbl 0878.13018
1997
Minimal resultant systems. Zbl 0856.13004
1995
A simple proof of Grothendieck’s theorem on the parafactoriality of local rings. Zbl 0813.13017
Call, Frederick; Lyubeznik, Gennady
1994
Finiteness properties of local cohomology modules (an application of $$D$$- modules to commutative algebra). Zbl 0795.13004
1993
Etale cohomological dimension and the topology of algebraic varieties. Zbl 0811.14014
1993
The number of defining equations of affine algebraic sets. Zbl 0770.14021
1992
A generalization of Lichtenbaum’s theorem on the cohomological dimension of algebraic varieties. Zbl 0724.14010
1991
On the vanishing of local cohomology modules. Zbl 0717.13011
Huneke, Craig; Lyubeznik, G.
1990
A survey of problems and results on the number of defining equations. Zbl 0753.14001
1989
On the arithmetical rank of monomial ideals. Zbl 0639.13015
1988
A new explicit finite free resolution of ideals generated by monomials in an R-sequence. Zbl 0652.13012
1988
The minimal non-Cohen-Macaulay monomial ideals. Zbl 0655.13020
1988
The number of generators of modules over polynomial rings. Zbl 0667.13006
1988
The number of equations needed to define an algebraic set. Zbl 0678.14012
1988
A property of ideals in polynomial rings. Zbl 0612.13008
1986
Some algebraic sets of high local cohomological dimension in projective space. Zbl 0587.14002
1985
On set-theoretic intersections. Zbl 0575.14041
1984
On the local cohomology modules $$H^ i_{{\mathfrak a}}(R)$$ for ideals $${\mathfrak a}$$ generated by monomials in an R-sequence. Zbl 0578.13012
1984
all top 5

### Cited by 357 Authors

 442 Commutative algebra (13-XX) 199 Algebraic geometry (14-XX) 38 Combinatorics (05-XX) 21 Associative rings and algebras (16-XX) 11 Several complex variables and analytic spaces (32-XX) 10 Algebraic topology (55-XX) 9 Category theory; homological algebra (18-XX) 4 Number theory (11-XX) 4 $$K$$-theory (19-XX) 4 Group theory and generalizations (20-XX) 4 Manifolds and cell complexes (57-XX) 4 Computer science (68-XX) 3 Order, lattices, ordered algebraic structures (06-XX) 3 Field theory and polynomials (12-XX) 2 History and biography (01-XX) 2 Convex and discrete geometry (52-XX) 2 Differential geometry (53-XX) 2 General topology (54-XX) 1 Ordinary differential equations (34-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Difference and functional equations (39-XX) 1 Approximations and expansions (41-XX) 1 Operations research, mathematical programming (90-XX)