  Shubnikov-de Haas and de Haas-van Alphen effects have been measured in the
underdoped high temperature superconductor YBa$_2$Cu$_3$O$_{6.51}$. Data are in
agreement with the standard Lifshitz-Kosevitch theory, which confirms the
presence of a coherent Fermi surface in the ground state of underdoped
cuprates. A low frequency $F = 530 \pm 10$ T is reported in both measurements,
pointing to small Fermi pocket, which corresponds to 2% of the first Brillouin
zone area only. This low value is in sharp contrast with that of overdoped
Tl$_2$Ba$_2$CuO$_{6+\delta}$, where a high frequency $F = 18$ kT has been
recently reported and corresponds to a large hole cylinder in agreement with
band structure calculations. These results point to a radical change in the
topology of the Fermi surface on opposing sides of the cuprate phase diagram.
