BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Gal Dor (Tel Aviv University) DTSTART:20210212T093000Z DTEND:20210212T103000Z DTSTAMP:20260423T024835Z UID:LAGA-AGAA/8 DESCRIPTION:Title: Monoidal structures on GL(2)-modules and abstractly automorphic represen tations\nby Gal Dor (Tel Aviv University) as part of Séminaire de gé ométrie arithmétique et motivique (Paris Nord)\n\n\nAbstract\nConsider t he function field $F$ of a smooth curve over $\\mathbf F_q$\, with $q \\ne q 2$.\n \n L-functions of automorphic representations of $\\GL(2)$ o ver $F$ are important objects for studying the arithmetic properties of th e field $F$. Unfortunately\, they can be defined in two different ways: on e by Godement-Jacquet\, and one by Jacquet-Langlands. Classically\, one sh ows that the resulting L-functions coincide using a complicated computatio n.\n \n Each of these L-functions is the GCD of a family of zeta int egrals associated to test data. I will categorify the question\, by showin g that there is a correspondence between the two families of zeta integral s\, instead of just their L-functions. The resulting comparison of test da ta will induce an exotic symmetric monoidal structure on the category of r epresentations of $\\GL(2)$.\n \n It turns out that an appropriate s pace of automorphic functions is a commutative algebra with respect to thi s symmetric monoidal structure. I will outline this construction\, and sho w how it can be used to construct a category of automorphic representation s.\n LOCATION:https://researchseminars.org/talk/LAGA-AGAA/8/ END:VEVENT END:VCALENDAR