Computations of sheaves associated to the representation theory of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msub><mml:mrow><mml:mi mathvariant="fraktur">sl</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math>

Stark, Jim

doi:10.1016/j.jalgebra.2014.03.001

Cited by 3 publications

(2 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Similarly one can check that the module Φ [0:1] (4) provides a counterexample to (4) ⇒ (1). See Stark [24] for the definition of Φ [0:1] (4) and additional sl 2 sheaf computations. Consider a p-nilpotent linear operator T : V → V .…”

Section: The Associated Sheaves Of a Modulementioning

confidence: 99%

Detecting projectivity in sheaves associated to representations of infinitesimal groups

Stark

2015

Journal of Pure and Applied Algebra

Self Cite

View full text Add to dashboard Cite

Let G be an infinitesimal group scheme of finite height r and V (G) the scheme which represents 1-parameter subgroups of G. We consider sheaves over the projective support variety P(G) constructed from a G-module M . We show that if P(G) is regular then the sheaf H [1] (M ) is zero if and only if M is projective. In general, H [1] defines a functor from the stable module category and we prove that its kernel is a thick triangulated subcategory. Finally, we give examples of G such that P(G) is regular and indicate, in characteristic 2, the connection to the BGG correspondence. Along the way we will provide new proofs of some known results and correct some errors in the literature.

show abstract

Section: The Associated Sheaves Of a Modulementioning

confidence: 99%

Detecting projectivity in sheaves associated to representations of infinitesimal groups

Stark

2015

Journal of Pure and Applied Algebra

Self Cite

View full text Add to dashboard Cite

show abstract

“…The projectivized support variety of Φ ξ (λ) contains one point: ξ. It is shown in [51] that for any finite dimensional restricted sl 2 -module M , Ker Θ M is a vector bundle, whether M has constant rank or not.…”

Section: Global P-nilpotent Operator and Vector Bundles On P(g)mentioning

confidence: 99%

Representations and cohomology of finite group schemes

Pevtsova

2014

Advances in Representation Theory of Algebras

View full text Add to dashboard Cite

This is a survey article covering developments in representation theory of finite group schemes over the last fifteen years. We start with the finite generation of cohomology of a finite group scheme and proceed to discuss various consequences and theories that ultimately grew out of that result. This includes the theory of one-parameter subgroups and rank varieties for infinitesimal group schemes; the π-points and Π-support spaces for finite group schemes, modules of constant rank and constant Jordan type, and construction of bundles on varieties closely related to Proj H • (G, k) for an infinitesimal group scheme G. The material is mostly complementary to the article of D. Benson on elementary abelian p-groups in the same volume; we concentrate on the aspects of the theory which either hold generally for any finite group scheme or are specific to finite group schemes which are not finite groups. In the last section we discuss varieties of elementary subalgebras of modular Lie algebras, generalizations of modules of constant Jordan type, and new constructions of bundles on projective varieties associated to a modular Lie algebra.

show abstract