Smooth representations, projective resolutions and cosheaves

Add to your list(s) Download to your calendar using vCal

• Katerina Hristova, University of Warwick
• Friday 24 November 2017, 15:00-16:00
• CMS, MR14.

If you have a question about this talk, please contact Nicolas Dupré.

For a locally compact totally disconnected topological group G one can define a ‘smooth’ representation. This is just a representation with an extra continuity condition. The category of all such representations is abelian, Noetherian and has enough projectives. In particular, one can study its projective dimension. In this talk we explain how to put a bound on the projective dimension of this category and moreover we show how to explicitly construct a projective resolution for each smooth G-module. The construction is inspired by a Theorem of Bernstein, who shows how this is done in the case of reductive p-adic groups. We generalise his approach to the case of an arbitrary locally compact totally disconnected group. However, the resolutions which Bernstein constructs are not of finitely generated projective modules. In the second part of the talk, following the work of Peter Schneider and Ulrich Stuhler for reductive algebraic groups, we explain how to construct finitely generated resolutions by passing to a category of G-equivariant objects, more precisely – a category of cosheaves on a simplicial complex on which G acts. Throughout we give examples of all our constructions for SL_n(Q_p) and GL_n(Q_p).

This talk is part of the Junior Algebra and Number Theory seminar series.

This talk is included in these lists:

• All CMS events
• All Talks (aka the CURE list)
• CMS Events
• CMS, MR14
• DPMMS Lists
• DPMMS Pure Maths Seminar
• DPMMS info aggregator
• DPMMS lists
• Hanchen DaDaDash
• Interested Talks
• Junior Algebra and Number Theory seminar
• School of Physical Sciences
• bld31
• ndb35's list

Note that ex-directory lists are not shown.