Weights and conservativity

The purpose of this article is to study conservativity in the context of triangulated categories equipped with a weight structure. As application, we establish (weight) conservativity for the restriction of the (generic) l-adic realization to the category of motives of Abelian type of characteristic zero.Comment: 22 pages; only few changes wrt. last version except for the numbering of the sections, which is now compatible with the published versio

Frobenius categories, Gorenstein algebras and rational surface singularities

We give sufficient conditions for a Frobenius category to be equivalent to the category of Gorenstein projective modules over an Iwanaga-Gorenstein ring. We then apply this result to the Frobenius category of special Cohen-Macaulay modules over a rational surface singularity, where we show that the associated stable category is triangle equivalent to the singularity category of a certain discrepant partial resolution of the given rational singularity. In particular, this produces uncountably many Iwanaga-Gorenstein rings of finite GP type. We also apply our method to representation theory, obtaining Auslander-Solberg and Kong type results.Comment: 27 pages, to appear in Comp. Mat

Grothendieck-Teichmueller group, operads and graph complexes: a survey

This paper attempts to provide a more or less self-contained introduction into theory of the Grothendieck-Teichmueller group and Drinfeld associators using the theory of operads and graph complexes.Comment: One reference is adde