Context. NGC 6397 is one of the most interesting, well-observed, and most thoroughly theoretically studied globular clusters. The existing wealth of observations allows us to study the reliability of the theoretical white dwarf cooling sequences of low-metallicity progenitors, to determine the age of NGC 6397 and the percentage of unresolved binaries. We also assess other important characteristics of the cluster, such as the slope of the initial mass function or the fraction of white dwarfs with hydrogen-deficient atmospheres.; Aims. We present a population synthesis study of the white dwarf population of NGC 6397. In particular, we study the shape of the color-magnitude diagram and the corresponding magnitude and color distributions.; Methods. To do this, we used an advanced Monte Carlo code that incorporates the most recent and reliable cooling sequences and an accurate modeling of the observational biases.; Results. Our theoretical models and the observed data agree well. In particular, we find that this agreement is best for those cooling sequences that take into account residual hydrogen burning. This result has important consequences for the evolution of progenitor stars during the thermally pulsing asymptotic giant branch phase, since it implies that appreciable third dredge-up in low-mass, low-metallicity progenitors is not expected to occur. Using a standard burst duration of 1.0 Gyr, we obtain that the age of the cluster is 12.8(-0.75)(+0.50) Gyr. Greater ages are also compatible with the observed data, but then unrealistic longer durations of the initial burst of star formation are needed to fit the luminosity function.; Conclusions. We conclude that a correct modeling of the white dwarf population of globular clusters, used in combination with the number counts of main-sequence stars, provides a unique tool for modeling the properties of globular clusters.

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