When does the fast end?
All fasts conclude after nightfall. This is defined as the sighting of three medium stars, or when the moon shines very brightly on the earth. It however does not suffice to see three large stars. [Practically, in Eretz Yisrael, some say that this is approximately 17 minutes after sunset by regular fasts and 24-27 minutes after sunset by Tishe Beav. Others say it is 27 minutes after sunset by all fasts of the winter, and 34-35 minutes after sunset by all fasts of the summer. According to the rulings of Rav Avraham Chaim Naah, nightfall in Eretz Yisrael is between 15-20 minutes after sunset in the winter and 20-26 minutes after sunset in the summer. In New York, some write one is to wait until 50 minutes after sunset, or at the very least 41 minutes after sunset. The Rebbe stated that in New York nightfall throughout the year is 36 minutes after sunset, both during the summer and winter. In all cases, one may begin Maariv before the above time, in order to conclude Maariv and be able to eat when the above time arrives. In such a case, one is to make sure to read Kerias Shema again after nightfall.]
 Michaber 562/1; See Piskeiy Teshuvos 562/1
 Michaber 562/1; Rosh; Rav Chisda in Taanis 12 “Whoever did not fast until sunset is not considered to have fasted.” Igros Moshe 4/10 rules that in New York one is to wait until 50 minutes after sunset, and at the very least wait 41 minutes.
Other opinions: Some Poskim rule it one is only required to fast until the start of Bein Hashmashos. [Sefas Emes Taanis 12; Aruch Hashuclhan 562/9 based on Rambam, Rashi, Ran] This however is in reference to Zman Rabbienu Tam, and not to the Zman of the Geonim. [Birur Halacha Tinyana 562; Piskeiy Teshuvos 562/1]
 Rama ibid; Hagahos Ashri; Hagahos Maimanis
 M”A 562/1 as corrected by Machatzis Hashekel ibid; Levushei Serud ibid; P”M 562 A”A 2
 Luach Eretz Yisrael of Harav Tukichinsky
 Sefer Birur Halacha, brought in Piskeiy Teshuvos 562/1
 See Ketzos Hashulchan 93 footnote 2; Shiureiy Tziyon of Grach Naah p. 76
 Igros Moshe 4/62; See Rebbe in Igros Kodesh 17/124 [printed in Shaareiy Halacha Uminhag 155 and Shulchan Menachem 2/123]
 Heard from Rabbi Leibal Groner; See Hiskashrus 370/19; Rav Raskin in Siddur p. 230
 Mateh Efraim 602/29; Igros Moshe ibid; Piskeiy Teshuvos 562/1 footnote 2; Rabbi Groner that so was directive of Rebbe to ask Rav Shmuel Levitan one year on a fast day to Daven before the time of nightfall and announce to everyone to say Shema again after nightfall; See Hiskashrus 1198