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SUMMARY:Regularized theta lifts and currents on products of Shimura curves
  - Luis Garcia (Imperial)
DTSTART:20140527T151500Z
DTEND:20140527T161500Z
UID:TALK51173@talks.cam.ac.uk
CONTACT:James Newton
DESCRIPTION:Consider two different holomorphic Hecke eigenforms $f_i \\in 
 \\pi_i$\, $i=1\,2$ of weight $2$ on a Shimura curve $X$ over a totally rea
 l field $F$. We will first discuss Beilinson's conjecture relating the ima
 ge of the complex regulator map from a higher Chow group with the special 
 value of  $L(\\pi_1 \\times \\pi_2\,s)$ at $s=0$. Then we will review Brui
 nier´s construction of meromorphic functions on $X$ with divisors support
 ed on CM points. Finally we will show how to use theta lifts of cusp forms
  on $Sp_4(\\mathbb{A}_F)$  to compute\, assuming that the $f_i$ have full 
 level and up to an archimedean zeta integral\, the period integrals arisin
 g as regulators of higher Chow cycles constructed using Bruinier's functio
 ns.
LOCATION:MR13
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