| Résume | In recent work with Tsai, we give a combinatorial formula for
Shalika germs of tamely ramified elements in GL_n over a non-archimedean
local F. This result has many corollaries, for example the polynomiality
of point-counts on local compactified Jacobians and a formula for the
orbital integrals of tamely ramified elements. The formula for Shalika
germs comes about by combining 1) an old algorithm by Waldspurger for
certain closely related germs with 2) ideas from the construction of
"superpolynomials" for algebraic knots using the elliptic Hall algebra,
which are more recent. I will explain the method together with some
examples and if there is time, discuss further directions such as a
canonical t-deformation of the Shalika germs. |
