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We consider the Bochner Laplacian on high tensor powers of a positive linebundle on a closed symplectic manifold (or, equivalently, the semiclassicalmagnetic Schr\"odinger operator with the non-degenerate magnetic field). Weassume that the operator has discrete wells. The main result of the paperstates asymptotic expansions for its low-lying eigenvalues.

Semiclassical eigenvalue asymptotics for the Bochner Laplacian of a positive line bundle on a symplectic manifold