PIRSA:20060027

Tate's thesis in the de Rham setting

APA

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

MLA

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

BibTex

          @misc{ 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}}
          }
          

Sam Raskin University of Texas - Austin

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.