arXiv subjects

Dave Benson

Publications and source records attributed to Dave Benson.

39 records · Page 3Linked to original sources

arXiv2008

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.

math.KT↗

arXiv2006

Detecting pro-p-groups that are not absolute Galois groups

We present several constraints on the absolute Galois groups G_F of fields F containing a primitive pth root of unity, using restrictions on the cohomology of index p normal subgroups from a previous paper by three of the authors. We first classify all maximal p-elementary abelian-by-order p quotients of such G_F. In the case p>2, each such quotient contains a unique closed index p elementary abelian subgroup. This seems to be the first case in which one can completely classify nontrivial quotients of absolute Galois groups by characteristic subgroups of normal subgroups. We then derive analogues of theorems of Artin-Schreier and Becker for order p elements of certain small quotients of G_F. Finally, we construct a new family of pro-p-groups which are not absolute Galois groups over any field F.

math.NT↗

arXiv2006

Detecting pro-p-groups that are not absolute Galois groups, expanded version

We present several constraints on the absolute Galois groups G_F of fields F containing a primitive pth root of unity, using restrictions on the cohomology of index p normal subgroups from a previous paper by three of the authors. We first classify all maximal p-elementary abelian-by-order p quotients of such G_F. In the case p>2, each such quotient contains a unique closed index p elementary abelian subgroup. This seems to be the first case in which one can completely classify nontrivial quotients of absolute Galois groups by characteristic subgroups of normal subgroups. We then derive analogues of theorems of Artin-Schreier and Becker for order p elements of certain small quotients of G_F. Finally, we construct new families of pro-p-groups which are not absolute Galois groups over any field F.

math.NT↗