Speaker: Simon Pepin Lehalleur
Date: 10:30 21/05/2021
Title: Exponential periods and exponential Voevodsky motives
Abstract:
Exponential periods are complex numbers defined in a similar way as
periods, by integration of functions on algebraic varieties defined
over number fields; the difference is that we allow a larger class of
functions which includes exponentials of regular functions.
Exponential periods form a ring which contains, besides classical
periods, new constants such as e, the Euler-Mascheroni constant,
special values of Gamma and Bessel functions, etc. Exponential periods
can also be expressed as matrix coefficients of a comparison
isomorphism between Betti and de Rham cohomology theories for
varieties with potential. This leads to the notion of exponential
motives and an exponential version of the
Grothendieck-Kontsevich-Zagier period conjecture. A version of the
theory using the framework of Nori motives was developed by
Fresán-Jossen. In this talk, I will explain a construction in the
setting of Voevodsky motives, which leads to a flexible notion of
families of exponential motives with a six operation formalism and a
Fourier transform. This is join work in progress with Javier Fresán
and Martin Gallauer.