Vukašin Mihajlović (Darmstadt): Central Sheaves for Ramified Groups

One of the main obstacles with trying to transfer classical results in geometric representation theory to the language of motives is the lack of a good notion of t-structure on the full category DM which would play the role of the perverse t-structure in the classical setting. However, when the spaces considered have stratifications with a nice enough geometry, one can still formulate some results motivically by restricting our category of motivic sheaves to certain nice subcategories, like those of Tate or Artin-Tate motives. However, these subcategories don’t automatically inherit the good categorical properties of DM, as they are not stable under the six operations. Here is where one needs to prove, by looking into the geometry of our problem more carefully, that the functors of interest to our setup do indeed preserve these subcategories. In this talk, we will do this for the case of the central functor applied to the BD Grassmannian of a twisted group.

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