The Bousfield lattice of a triangulated category and stratification

For a tensor triangulated category which is well generated in the sense of Neeman, it is shown that the collection of Bousfield classes forms a set. This set has a natural structure of a complete lattice which is then studied, using the notions of stratification and support.Comment: 25 pages; minor changes from earlier version; this will appear in the Math.

Localising subcategories for cochains on the classifying space of a finite group

The localising subcategories of the derived category of the cochains on the classifying space of a finite group are classified. They are in one to one correspondence with the subsets of the set of homogeneous prime ideals of the cohomology ring $H^*(G,k)$.Comment: 5 pages, minor changes, accepted for publication in C. R. Math. Acad. Sci. Pari

Local cohomology and support for triangulated categories

We propose a new method for defining a notion of support for objects in any compactly generated triangulated category admitting small coproducts. This approach is based on a construction of local cohomology functors on triangulated categories, with respect to a central ring of operators. Suitably specialized one recovers, for example, the theory for commutative noetherian rings due to Foxby and Neeman, the theory of Avramov and Buchweitz for complete intersection local rings, and varieties for representations of finite groups according to Benson, Carlson, and Rickard. We give explicit examples of objects whose triangulated support and cohomological support differ. In the case of group representations, this allows us to correct and establish a conjecture of Benson.Comment: 40 pages. Relatively minor changes (clarifications, corrections, new references, etc). This article will appear in the Ann. Sci. Ecole Norm. Su

Stratifying modular representations of finite groups

We classify localising subcategories of the stable module category of a finite group that are closed under tensor product with simple (or, equivalently all) modules. One application is a proof of the telescope conjecture in this context. Others include new proofs of the tensor product theorem and of the classification of thick subcategories of the finitely generated modules which avoid the use of cyclic shifted subgroups. Along the way we establish similar classifications for differential graded modules over graded polynomial rings, and over graded exterior algebras.Comment: 37 pages; minor changes from the first version. This is slated to appear in the January 2012 issue of Annals of Math., volume 175, no.

Colocalizing subcategories and cosupport

The Hom closed colocalizing subcategories of the stable module category of a finite group are classified. Along the way, the colocalizing subcategories of the homotopy category of injectives over an exterior algebra, and the derived category of a formal commutative differential graded algebra, are classified. To this end, and with an eye towards future applications, a notion of local homology and cosupport for triangulated categories is developed, building on earlier work of the authors on local cohomology and support.Comment: 38 pages; minor changes; to appear in J. Reine. Angew. Mat

Parallax measurements of cool brown dwarfs

Accurate parallax measurements allow us to determine physical properties of brown dwarfs, and help us to constrain evolutionary and atmospheric models, break the age-mass degeneracy and reveal unresolved binaries. We measured absolute trigonometric parallaxes and proper motions of 6 cool brown dwarfs using background galaxies to establish an absolute reference frame. We derive the absolute J-mag. The six T brown dwarfs in our sample have spectral types between T2.5 and T7.5 and magnitudes in J between 13.9 and 18.0, with photometric distances below 25 pc. The observations were taken in the J-band with the Omega-2000 camera on the 3.5 m telescope at Calar Alto, during a time period of 27 months, between March 2011 and June 2013. The number of epochs varied between 11 and 12 depending on the object. The reduction of the astrometric measurements was carried out with respect to the field stars. The relative parallax and proper motions were transformed into absolute measurements using the background galaxies in our fields. We obtained absolute parallaxes for our six brown dwarfs with a precision between 3 and 6 mas. We compared our results in a color-magnitude diagram with other brown dwarfs with determined parallax and with the BT-Settl 2012 atmospheric models. For four of the six targets we found a good agreement in luminosity with objects of similar spectral types. We obtained an improved accuracy in the parallaxes and proper motions in comparison to previous works. The object 2MASS J11061197+2754225 is more than 1 mag overluminous in all bands pointing to binarity or high order multiplicity.Comment: 9 pages, 15 figures. Astronomy & Astrophysics, 201