From Israel National News, 17 December 2010, by Maayana Miskin:
Friday is the tenth day of the Hebrew month of Tevet, a fast day on which Jews remember the siege of Jerusalem that preceded the destruction of the First Temple and the Babylonian exile.
The siege is described in the Bible in the Book of Kings.
The day is also the time at which mourning prayers are said for Holocaust victims whose date of death is not known. Many religious Jews mourn the Holocaust on the 10th of Tevet rather than on the date chosen by the Israeli government in the Hebrew month of Nissan.
The tenth of Tevet is observed as a fast from morning until nightfall. It is the only day-long fast day that can fall on a Friday.
Another event that is mourned on the 10th of Tevet is the day on which King Ptolemy of Egypt forced Jewish scholars to translate the Hebrew Bible into Greek. Their translation was used by those who sought to assimilate Jews into Greek culture, and later formed the basis of the Christian Bible, which for many centuries was used to promote persecution of Jews.
Yet another is the death of Ezra the Scribe, who led Jews back to Israel from their exile in Babylon and directed the construction of the Second Temple.