19 décembre 2017

Andrea D'Agnolo (Padova)
A microlocal approach to the enhanced Fourier-Sato transform in dimension one

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Lieu : IMO (Bât. 307), salle 0A4

Résumé : Let M be a holonomic algebraic D-module on the affine line. Its exponential factors
are Puiseux germs describing the growth of holomorphic solutions to M at irregular points. The
stationary phase formula states that the non linear exponential factors of the Fourier transform
of M are obtained by Legendre transform from the non linear exponential factors of M. We
give a microlocal proof of this fact, by translating it in terms of enhanced perverse sheaves
through the Riemann-Hilbert correspondence. (This is joint work with Masaki Kashiwara.)

A microlocal approach to the enhanced Fourier-Sato transform in dimension one  Version PDF