PIRSA:20060027 Conference Mathematical physics

DOI10.48660/20060027

Conference/School: Geometric Representation Theory

Raskin, S. (2020). Tate's thesis in the de Rham setting. Perimeter Institute. https://pirsa.org/20060027

Raskin, Sam. Tate's thesis in the de Rham setting. Perimeter Institute, Jun. 22, 2020, https://pirsa.org/20060027 

@misc{ pirsa_PIRSA:20060027,
  doi = {10.48660/20060027},
  url = {https://pirsa.org/20060027},
  author = {Raskin, Sam},
  keywords = {Mathematical physics},
  language = {en},
  title = {Tate{\textquoteright}s thesis in the de Rham setting},
  publisher = {Perimeter Institute},
  year = {2020},
  month = {jun},
  note = {PIRSA:20060027 see, \url{https://pirsa.org}}
}

Abstract

This is joint work with Justin Hilburn. We will explain a theorem showing that D-modules on the Tate vector space of Laurent series are equivalent to ind-coherent sheaves on the space of rank 1 de Rham local systems on the punctured disc equipped with a flat section. Time permitting, we will also describe an application of this result in the global setting. Our results may be understood as a geometric refinement of Tate's ideas in the setting of harmonic analysis. They also may be understood as a proof of a strong form of the 3d mirror symmetry conjectures: our results amount to an equivalence of A/B-twists of the free hypermultiplet and a U(1)-gauged hypermultiplet.

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