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SUMMARY:Ryan Chen (MIT)
DTSTART:20240305T210000Z
DTEND:20240305T220000Z
DTSTAMP:20260423T130232Z
UID:MITNT/88
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITNT/88/">C
 o-rank 1 Arithmetic Siegel–Weil</a>\nby Ryan Chen (MIT) as part of MIT n
 umber theory seminar\n\nLecture held in Room 2-449 in the Simons Building 
 (building 2).\n\nAbstract\nI will introduce my recent work on an arithmeti
 c Siegel–Weil formula for Kudla–Rapoport $1$-cycles on integral models
  of some unitary Shimura varieties. This formula implies that degrees of K
 udla–Rapoport arithmetic special $1$-cycles are encoded in the first der
 ivatives of unitary Eisenstein series Fourier coefficients. In the simples
 t case\, this can be rephrased in terms of Faltings heights of Hecke trans
 lates of CM elliptic curves\, and the classical weight $2$ Eisenstein seri
 es.\n\nThe key input is a new local limiting method which relates (a) degr
 ees of local special 0-cycles and (b) local contributions to heights of sp
 ecial $1$-cycles.\n
LOCATION:https://researchseminars.org/talk/MITNT/88/
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