Resolution of singularities on the Lubin-Tate tower

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

• Jared Weinstein (UCLA)
• Tuesday 18 May 2010, 14:30-15:30
• MR13.

If you have a question about this talk, please contact Tom Fisher.

A fundamental result in local class field theory is the 1965 paper of Lubin and Tate, which classifies the abelian extensions of a nonarchimedean local field in terms of an algebraic structure known as a one-dimensional formal module. We’ll review this result, and show how the question of constructing nonabelian extensions leads to the study of the Lubin-Tate tower, which can be viewed as an infinitesimal version of the classical tower of modular curves X(pⁿ).

By results of Harris-Taylor and Boyer, the cohomology of the Lubin-Tate tower encodes precise information about non-abelian extensions of the local field (namely, it realizes the local Langlands correspondence). The Lubin-Tate tower has a horribly singular special fiber, which hinders any direct study of its cohomology, but we will show that after blowing up a singularity there is a model for the tower whose reduction contains a very curious nonsingular hypersurface defined over a finite field—curious because it seems to have the maximum number of rational points relative to its topology. We will write down the equation for this hypersurface and formulate a conjecture (alas, still unproved) regarding its zeta function.

This talk is part of the Number Theory Seminar series.

This talk is included in these lists:

• All CMS events
• All Talks (aka the CURE list)
• CMS Events
• DPMMS Lists
• DPMMS Pure Maths Seminar
• DPMMS info aggregator
• DPMMS lists
• Hanchen DaDaDash
• Interested Talks
• MR13
• Number Theory Seminar
• School of Physical Sciences
• bld31

Note that ex-directory lists are not shown.