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SUMMARY:An arithmetic Riemann-Roch theorem on modular curves via heat kern
 el regularization
DTSTART:20180704T150000
DTEND:20180704T160000
DTSTAMP:20260408T105206Z
UID:6b3e959e828b9d8d3c67542c88e137aac293c3c5d2dd520c209f4c30
CATEGORIES:Conferences - Seminars
DESCRIPTION:Jürg Kramer (Humboldt-Universität zu Berlin)\nThe arithmetic
  Riemann{Roch theorem has been established by H. Gillet/C. Soule as well a
 s by G. Faltings for projective and generically smooth morphisms f : X->Y 
 of arithmetic varieties and hermitian vector bundles E = (E \; k k) equipp
 ed with smooth hermitian metrics. In our talk\, we will present a variant 
 of an arithmetic Riemann{Roch theorem in a singular setting\, namely\, the
  case of the line bundle of modular forms of weight k (an even integer) on
  (regular\, projective models of) modular curves equipped with the Peterss
 on metric\, which becomes logarithmically singular at the cusps. The proof
  starts from the known arithmetic Riemann-Roch formula for smooth hermitia
 n metrics approximating the hyperbolic metric under consideration and then
  proceeds with an investigation of the degeneration behavior of the starti
 ng formula using heat kernel regularization techniques while the smoothene
 d metric approaches the singular metric.
LOCATION:MA A3 31
STATUS:CONFIRMED
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