Endoscopie et conjecture raffin\'ee de Gan-Gross-Prasad pour les groupes   unitaires
  Under endoscopic assumptions about $L$-packets of unitary groups, we prove the local Gan-Gross-Prasad conjecture for tempered representations of unitary groups over $p$-adic fields. Roughly, this conjecture says that branching laws for $U(n-1)\subset U(n)$ can be computed using epsilon factors. 
Rapha\"el Beuzart-Plessis (IMJ)
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