BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Michele Fornea (Columbia University) DTSTART:20220629T090000Z DTEND:20220629T100000Z DTSTAMP:20260423T021344Z UID:NTUniPD/13 DESCRIPTION:Title: Plectic Jacobians and Hodge theory\nby Michele Fornea (Columbia Unive rsity) as part of Number Theory Seminars at Università degli Studi di Pad ova\n\n\nAbstract\nGehrmann\, Guitart\, Masdeu and myself recently propose d\, and gave evidence for\, plectic generalizations of Stark-Heegner point s. The construction is p-adic\, cohomological\, and unfortunately lacking a satisfying geometric interpretation. Nevertheless\, we formulated precis e conjectures on the algebraicity of plectic points and their significance for the arithmetic of higher rank elliptic curves.\nIn this talk I will r eport on work in progress on the Archimedean side of the story where geome try has a prominent role:\nI will describe a collection of complex tori — called plectic Jacobians — associated with the plectic Hodge struct ure appearing in the middle degree cohomology of Hilbert modular varieties . Interestingly\, the Oda-Yoshida conjecture can be used to prove that ple ctic Jacobians are modular abelian varieties defined over $\\overline{\\ma thbb{Q}}$. Moreover\, the existence of exotic Abel-Jacobi morphisms (mappi ng zero-cycles to plectic Jacobians) further highlights the arithmetic app eal of the construction.\n LOCATION:https://researchseminars.org/talk/NTUniPD/13/ END:VEVENT END:VCALENDAR