  Reconstruction of the Fermi surface of high-temperature superconducting
cuprates in the pseudogap state is analyzed within nearly exactly solvable
model of the pseudogap state, induced by short-range order fluctuations of
antiferromagnetic (AFM, spin density wave (SDW), or similar charge density wave
(CDW)) order parameter, competing with superconductivity. We explicitly
demonstrate the evolution from "Fermi arcs" (on the "large" Fermi surface)
observed in ARPES experiments at relatively high temperatures (when both the
amplitude and phase of density waves fluctuate randomly) towards formation of
typical "small" electron and hole "pockets", which are apparently observed in
de Haas - van Alfen and Hall resistance oscillation experiments at low
temperatures (when only the phase of density waves fluctuate, and correlation
length of the short-range order is large enough). A qualitative criterion for
quantum oscillations in high magnetic fields to be observable in the pseudogap
state is formulated in terms of cyclotron frequency, correlation length of
fluctuations and Fermi velocity.
