BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Shiva Chidambaram (University of Chicago) DTSTART:20210208T210000Z DTEND:20210208T220000Z DTSTAMP:20260423T021413Z UID:AGSAGS/17 DESCRIPTION:Title: Moduli spaces of low dimensional abelian varieties with torsion\nby Sh iva Chidambaram (University of Chicago) as part of American Graduate Stude nt Algebraic Geometry Seminar\n\n\nAbstract\nThe Siegel modular variety $A _2(3)$ which parametrizes abelian surfaces with split level 3 structure is birational to the Burkhardt quartic threefold. This was shown to be ratio nal over $\\mathbb{Q}$ by Bruin and Nasserden. What can we say about its t wist $A_2(\\rho)$ for a Galois representation $\\rho$ valued in $GSp(4\, F _3)$? While it is not rational in general\, it is unirational over $\\math bb{Q}$ by a map of degree at most 6\, showing that $\\rho$ arises as the 3 -torsion of infinitely many abelian surfaces. In joint work with Frank Cal egari and David Roberts\, we obtain an explicit description of the univers al object over a degree 6 cover using invariant theoretic ideas. Similar i deas work for $(g\,p) = (1\,2)\, (1\,3)\, (1\,5)\, (2\,2)\, (2\,3)$ and $( 3\,2)$. When $(g\,p)$ is not one of these six tuples\, we discuss a local obstruction for representations to arise as torsion.\n LOCATION:https://researchseminars.org/talk/AGSAGS/17/ END:VEVENT END:VCALENDAR