Complete intersections and derived categories (2009)
Benson, D. J., Greenlees, J. P. C.
We propose a definition of when a triangulated category should be considered a complete intersection. We show (using work of Avramov and Gulliksen) that for the derived category of a complete local...
Complete intersections and rational homotopy theory (2009)
Greenlees, J. P. C., Hess, K., Shamir, S.
We investigate various homotopy invariant formulations of commutative algebra in the context of rational homotopy theory. The main subject is the complete intersection condition, where we show that a...
Gross-Hopkins duality and the Gorenstein condition (2009)
Dwyer, W. G., Greenlees, J. P. C., Iyengar, S. B.
Gross and Hopkins have proved that in chromatic stable homotopy, Spanier-Whitehead duality nearly coincides with Brown-Comenetz duality. Our goal is to give a conceptual interpretation for this...
Poincare duality for K-theory of equivariant complex projective spaces (2008)
Greenlees, J.P.C., Williams, G.R.
We make explicit Poincare duality for the equivariant K-theory of equivariant complex projective spaces. The case of the trivial group provides a new approach to the K-theory orientation.
Rational torus-equivariant homotopy I: calculating groups of stable maps (2008)
We construct an abelian category A(G) of sheaves over a category of closed subgroups of the r-torus G and show it is of finite injective dimension. It can be used as a model for rational $G$-spectra...
Poincar\'e duality for $K$-theory of equivariant complex projective spaces (2007)
Greenlees, J. P. C., Williams, G. R.
We make explicit Poincar\'{e} duality for the equivariant $K$-theory of equivariant complex projective spaces. The case of the trivial group provides a new approach to the $K$-theory orientation.
Rational torus-equivariant homotopy I: calculating groups of stable maps (2007)
We construct an abelian category A(G) of sheaves over a category of closed subgroups of the r-torus G and show it is of finite injective dimension. It can be used as a model for rational $G$-spectra...
Circle-equivariant classifying spaces and the rational equivariant sigma genus (2007)
Ando, Matthew, Greenlees, J. P. C.
We analyze the circle-equivariant spectrum MString_C which is the equivariant analogue of the cobordism spectrum MU of stably almost complex manifolds with c_1=c_2=0. The second author has shown how...
Circle-equivariant classifying spaces and the rational equivariant sigma genus (2007)
We analyze the circle-equivariant spectrum MString_C which is the equivariant analogue of the cobordism spectrum MU of stably almost complex manifolds with c_1=c_2=0. The second author has shown how...
First steps in brave new commutative algebra (2007)
This is an expository account of completion and local cohomology in brave new commutative algebra, especially as it applies to completion theorems and their duals in equivariant topology. The first...
Spectra for commutative algebraists (2007)
The article is designed to explain to commutative algebraists what spectra (in the sense of algebraic topology) are, why they were originally defined, and how they can be useful for commutative...
Spectra for commutative algebraists (2006)
The article is designed to explain to commutative algebraists what spectra (in the sense of algebraic topology) are, why they were originally defined, and how they can be useful for commutative...
First steps in brave new commutative algebra (2006)
This is an expository account of completion and local cohomology in brave new commutative algebra, especially as it applies to completion theorems and their duals in equivariant topology. The first...
Duality in algebra and topology (2006)
Dwyer, W.G., Greenlees, J.P.C., Iyengar, S.
In this paper we take some classical ideas from commutative algebra, mostly ideas involving duality, and apply them in algebraic topology. To accomplish this we interpret properties of ordinary...
Finiteness in derived categories of local rings (2006)
Dwyer, W., Greenlees, J.P.C., Iyengar, S.
New homotopy invariant finiteness conditions on modules over commutative rings are introduced, and their properties are studied systematically. A number of finiteness results for classical...
Rational S^1-equivariant elliptic cohomology (2005)
For each elliptic curve A over the rational numbers we construct a 2-periodic S^1-equivariant cohomology theory E whose cohomology ring is the sheaf cohomology of A; the homology of the sphere of the...
Duality in algebra and topology (2005)
Dwyer, W. G., Greenlees, J. P. C., Iyengar, S.
In this paper we take some classical ideas from commutative algebra, mostly ideas involving duality, and apply them in algebraic topology. To accomplish this we interpret properties of ordinary...
Rational S^1-equivariant elliptic cohomology (2005)
For each elliptic curve A over the rational numbers we construct a 2-periodic S^1-equivariant cohomology theory E whose cohomology ring is the sheaf cohomology of A; the homology of the sphere of the...
Equivariant version of real and complex connective $K$-theory (2005)
We survey available results on the construction and calculation of equivariant versions of real and complex connective K-theory.
Finiteness in derived categories of local rings (2004)
Dwyer, W., Greenlees, J. P. C., Iyengar, S.
New homotopy invariant finiteness conditions on modules over commutative rings are introduced, and their properties are studied systematically. A number of finiteness results for classical...
The universality of equivariant complex bordism (2002)
Kriz, Igor, Cole, Michael, Greenlees, J.P.C.
We show that if A is an abelian compact Lie group, all A -equivariant complex vector bundles are orientable over a complex orientable equivariant cohomology theory. In the process, we calculate the...
Equivariant formal group laws and complex oriented cohomology theories (2001)
The article gives an introduction to equivariant formal group laws, and explains its relevance to complex oriented cohomology theories in general and to complex cobordism in particular.
Complete intersections and rational homotopy theory
Greenlees, J. P. C., Hess, K., Shamir, S.
We investigate various homotopy invariant formulations of commutative algebra in the context of rational homotopy theory. The main subject is the complete intersection condition, where we show that a...