Gemara

(Abaye): If one served idolatry due to love or fear, he is liable, for in any event he served.

(Rava): He is exempt, for he did not accept it to be his god.

74a (R. Yochanan): If one is told to transgress or else be killed, he may (or must) transgress, except for dolatry, Arayos, and murder.

(Beraisa - R. Eliezer): "Uv'Chol Nafshecha" obligates loving Hash-m with all his life (he may not transgress idolatry, even to save his life).

Reasoning teaches about murder. You do not know whether you are more worthy to live than another person!

(Beraisa - Rebbi): "Ki ka'Asher... u'Rtzacho Nafesh" equates Na'arah Me'orasah to a murderer. One may not transgress either to save his life.

(Rav Dimi): We transgress (all other Mitzvos) to save a life. This is not at a time of Shemad (a royal decree against Mitzvos). At a time of Shemad, one may not transgress even a light Mitzvah. He must submit to be killed.

(Ravin): One may not transgress if 10 Yisre'elim are present.

Question: Esther was married to Achashverosh in public (i.e. many Yisraelim knew about it. She should have refused and forfeited her life)!

Answer #1 (Abaye): She was Karka Olam (passive, until she went to the king on Mordechai's command. In such a case, one need not forfeit his life).

Answer #2 (Rava): When the Nochri wants the Yisrael to transgress for the Nochri's benefit, even in public, one need not forfeit his life.

Support (Rava, for himself): On their idolatrous festivals, Nochrim demand that we give them coals. Even though this pertains to idolatry, we do not forfeit our lives! Because they intend for their own benefit, it is permitted.

75a (Rav Yehudah): Once, a man became sick due to desire for a woman. Doctors said that he will recover only if he has Bi'ah with her. Rabanan forbade this. The doctors suggested that perhaps it will help if she stands naked in front of him, or talks with him in back of the fence. Rabanan did not permit.

R. Yakov bar Idi or R. Shmuel bar Nachmani said that Rabanan were stringent because she was married. The other said that she was single. Rabanan were stringent to avoid shame to her family, or to uphold Kedushas Bnos Yisrael.

Pesachim 25a (Ravin citing R. Yochanan): One may heal through any means, except through idolatry, Arayos or murder.

Rishonim

Rambam (Hilchos Yesodei ha'Torah 5:1,2): All of Yisrael are commanded to Mekadesh Hash-m and not Mechalel Hash-m. If a Nochri threatens a Yisrael to transgress a Mitzvah or be killed, if the Nochri seeks his own benefit, e.g. to have Bi'ah with a Bas Yisrael, or a Yisrael should work for him on Shabbos, the Yisrael should transgress and not be killed. However, for idolatry, Arayos and murder, he must submit to death and not transgress;

If the Nochri seeks to make the Yisrael transgress, the Yisrael should comply unless 10 Yisraelim are present.

Question (Nimukei Yosef DH v'Im Tomar): We asked that Esther should have refused to have relations with Achashverosh, since it was known. Even in private, one must be Moser Nefesh for Arayos!

Answer #1 (Kesef Mishneh): The Rambam rules like Rava. He holds like the Ramban, that Bi'ah with a Nochri is not considered Arayos. If it were, it would be forbidden even if the Nochri intends for his own benefit. The Rambam does not hold like the one who expounds 'l'Vas' to teach that Esther was married to Mordechai.

Objection (Nimukei Yosef ibid.): Bi'as Yisrael with a Nochris is not Arayos, but Bi'as Nochri with a Yisraelis is Arayos. A Nochri is killed for a Na'arah Me'orasah (Yisraelis - Sanhedrin 57b), and also she is killed. Why wasn't Esther Moser Nefesh according to the opinion that she was married to Mordechai?

Answer #2 (Nimukei Yosef): One need not be Moser Nefesh if the Nochri can physically force him to do the Aveirah, since perhaps in any case the Aveirah will be done. This applies even to the three severe Aveiros.

Gra (YD 157:10): Karka Olam means that she can be forced to do the Aveirah against her will.

Answer #3 (Rosh 8:3 and Tosfos Yoma 82a DH Mah): One need not be Moser Nefesh if he is 'Karka Olam', i.e. passive. The Gemara knew that Karka Olam exempts from Mesiras Nefesh for Arayos. We learn Arayos from murder, and the source for Mesiras Nefesh for murder (you do not know if you are more worthy than him) applies only to doing an action. It asked about Kidush Hash-m, and answered that Karka Olam exempts even regarding Kidush Hash-m.

Tosfos Yom ha'Kipurim (82a DH Kasvu Od): The Rambam and Shulchan Aruch do not make such a distinction. It appears that they hold that Karka Olam does not exempt from Mesiras Nefesh for the three Aveiros.

Poskim

Shulchan Aruch (YD 157:1): If a Nochri threatens a Yisrael to transgress a Mitzvah or be killed, for any Mitzvah other than idolatry, Arayos and murder, in private, the Yisrael should transgress. If the Nochri intends is to make the Yisrael transgress, the Yisrael may be stringent and submit to be killed.

Avnei Nezer (YD 128:4, 131:5): Why does the Rambam say that Kidush Hash-m obligates Mesiras Nefesh for the three Aveiros? Kidush Hash-m applies to the other Mitzvos in public. We learn the three Aveiros from "v'Ohavta", reasoning and a Hekesh! The Rambam forbids curing oneself through idolatry due to v'Ohavta. Semak says that v'Ohavta forbids idolatry in private (even for Piku'ach Nefesh), and v'Nikdashti forbids other Mitzvos in public. Tosfos (61b DH Rava) asked, since Rava exempts one who serves idolatry due to love or fear, why must one be Moser Nefesh rather than serve due to fear? The Rambam answers that since it looks to the Nochri who coerced him as if he serves, he transgresses v'Ohavta, and it is Chilul Hash-m in the Nochri's eyes. Piku'ach Nefesh overrides other Aveiros, so Chilul Hash-m does not apply. [Magihah - if there is no one else present, why is it Chilul Hash-m? The Nochri knows that he is coerced!] Even if a Nochri is commanded about Kidush Hash-m, he need not be Moser Nefesh for idolatry in private, for he is not commanded v'Ohavta.

Ba'al ha'Ma'or (18a): One may not use idolatry for a cure, even in a case of mortal danger. Mortal danger did not permit even a small Hana'ah (talking in back of the fence) with a woman. According to the opinion that she was married, this was not a special enactment for Kedushas Benos Yisrael! Idolatry and murder are always forbidden, Arayos is more lenient. We permit when the Me'anes seeks his own pleasure. Mesiras Nefesh for Ervah is when others demand that he have Bi'ah with her, but not when she forces him for her Hana'ah. Other Aveiros are permitted even if the Me'anes intends to make him transgress, unless it is a time of Shemad or in public.

Hagbahas ha'Bach (10): Ba'al ha'Ma'or forbids when one wants to benefit from the Aveirah itself. The Ran and Nimukei Yosef agree.

Suggestion: We learn from Sanhedrin 75a that letter of the law, one must forfeit his life rather than benefit from Ervah. The same applies to going in a place where women are not covered properly, e.g. the beach.

Rebuttal (Igros Moshe EH 1:56): One may not derive this from the Ba'al ha'Ma'or. There, he wanted to benefit from Ervah to cure his lust for sin. This is more severe that saving oneself from a Me'anes who commands him to have Bi'ah. The Ba'al ha'Ma'or is more lenient when the Me'anes seeks his own pleasure, and permits even for Arayos, even though one may not benefit to cure himself from his lust. We permit for other Aveiros, e.g. one who lusts to eat a Neveilah or on Yom Kipur. One may not look at her naked to cure himself, even though it is not Isur Mamash (perhaps this means what the Torah forbade - PF). If he was threatened to look at her or be killed, perhaps it is permitted, since he need not touch her. The Ramban equates these, for he holds that Kidush Hash-m applies to the three Aveiros even in private. When the Me'anes intends for his own pleasure, Kidush Hash-m does not apply. This shows that Mesiras Nefesh for them is due to their severity. Also the Ramban could permit standing naked in front of him, which is not Isur Mamash. It seems that the Ba'al ha'Ma'or holds that since Kidush Hash-m applies to these three Aveiros, transgressing for desire is Chilul Hash-m, and obligates Mesiras Nefesh. Desire for other Aveiros is not Chilul Hash-m. One desires Neveilah (or eating on Yom Kipur) just like he desires Kosher meat (or eating on another day). Therefore, Piku'ach Nefesh overrides other Mitzvos even in public, like for any sick person. If one desires a particular woman who is Asur to him, we suspect that it is because she is forbidden, and that is why he is mortally sick. This is Chilul Hash-m. The Ramban holds that perhaps he simply desires her, and not due to the Isur.

Igros Moshe (ibid.): We cannot prove that one must be Moser Nefesh to avoid looking at Ervah. If one does not intend to benefit from looking, it is a light Isur. Without desire, there is no Lav or lashes even for touching, hugging and kissing Shach (157:10). Also the Rambam connotes like this. The Isur is lighter without desire, so even if there is some lust it is lighter than looking with intent to benefit, so we cannot derive a Chiyuv for Mesiras Nefesh. Also, the Isur Arayos of looking is like Sanhedrin 75a, when she comes for him to look at her. When he goes to where women are naked, the Isur is bringing himself to Hirhur, which could lead to a seminal emission.