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UID:20260602T200419EDT-5351pVHtsn@132.216.98.100
DTSTAMP:20260603T000419Z
DESCRIPTION:On the p-adic variation of the Gross-Kohnen-Zagier theorem.\n\n
 Given an elliptic curve defined over the field of rational numbers and giv
 en an imaginary quadratic field K\, one may define (using the theory of co
 mplex multiplication) a K-rational point of the elliptic curve\, called He
 egner point. Heegner points are crucial tools for studying the arithmetic 
 of elliptic curves\; in particular\, the celebrated theorem of Gross and Z
 agier relates\, under suitable arithmetic assumptions\, the Neron-Tate hei
 ght of Heegner points and the leading term of the complex L-function of E 
 over K. The Gross-Kohnen-Zagier theorem (GKZ)\, complementary to the Gross
 -Zagier theorem mentioned above\, shows that\, under suitable arithmetic a
 ssumptions\, the relative positions of the Heegner points\, as the imagina
 ry quadratic field varies while the elliptic curve stays fixed\, are encod
 ed by the Fourier coefficients of a Jacobi form. Briefly\, Heegner points 
 are generating series for Jacobi forms. Several generalizations of the GKZ
  theorem are available in the literature\, by Kudla (putting things in a g
 eneral perspective by the formulation of a series of conjectures\, known a
 s Kudla's program)\, Borcherds (using singular theta liftings) and Yuan-Zh
 ang-Zhang (in the automorphic representation setting). In this seminar I w
 ill try to explore a further possible direction suggested by the GKZ theor
 em\, where we make all objects vary in p-adic analytic families. This is a
  joint work with M.-H. Nicole. \n
DTSTART:20171123T153000Z
DTEND:20171123T170000Z
LOCATION:Room 920\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue 
 Sherbrooke Ouest
SUMMARY:Matteo Longo\, University of Padova
URL:/mathstat/channels/event/matteo-longo-university-p
 adova-282949
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