Gemara

A woman can be divorced against her will.

90a (Mishnah - Beis Shamai): One may divorce his wife only if "he found in her Ervah (immorality)";

Beis Hillel say, even if she burned the food, he may divorce her - "he found in her Ervas (or) Davar (a matter)";

R. Akiva permits even if he found a prettier woman - "if she does not find grace in his eyes."

Question (Rav Papa): If he found neither Ervah nor a Davar and divorced her, what is the law?

Answer (Rava): One who raped a woman "may not divorce her all his days." If he did, he is always commanded to remarry her. Here, he need not remarry her.

(Beraisa - R. Meir): If one's wife goes out with uncovered hair, weaves in public with her elbows exposed, or bathes where men bathe, it is a Mitzvah to divorce her.

Kesuvos 51a (Mishnah): If a wife gets sick, her husband must heal her. He may not say 'behold I divorce her. Here is a Get and her Kesuvah, let her heal herself.'

Rishonim

The Rif and Rosh (50b and 9:15) bring the Gemara on 90a.

Rambam (Hilchos Gerushin 10:22): It is a Mitzvah to divorce a woman with evil tenets, or one who is not modest like proper Bnos Yisrael.

Hagahos Mishneh l'Melech (21): Keneses ha'Gedolah says that there is no Mitzvah, mid'Oraisa or mid'Rabanan, not to divorce. Even Beis Shamai merely counsel not to. A proof is that R. Gershom needed to enact to forbid divorcing a woman b'Al Korchah (against her will). Also, we permit one who swore to divorce his wife to do so. Several Acharonim agree. I am astounded. Rav Papa asked if one who divorced without proper reason is obligated to remarry her! The Rashba (Teshuvah 18) says that no Berachah was enacted for divorce, for sometimes it is forbidden, e.g. he did not find Ervah in her. We infer that also Beis Hillel forbid divorcing without a reason. The Isur is only mid'Rabanan. We learned (Sanhedrin 22a) that divorce is very harsh, for they permitted David to be secluded with Avishag, but they did not permit him to divorce one of his wives (to enable him to marry her). This is no proof if the Torah forbids divorce, since seclusion is forbidden only mid'Rabanan.

Hagahos Ashri (Kidushin 3:16): If one said 'my wife was Mezanah', he is not believed to forbid her. Perhaps he seeks to marry another woman, and according to R. Gershom's decree he cannot divorce his current wife b'Al Korchah. Therefore, we excommunicate one who forbids his wife to himself and divorces her b'Al Korchah, for he is Mevatel the decree.

Poskim

Shulchan Aruch (EH 119:6): One can divorce a woman without her Da'as.

Rashba (Teshuvah 1654) and Tashbatz (3:223, cited in Beis Yosef DH Kasuv bi'Teshuvos): A Gaon forbids divorcing a woman b'Al Korchah if he cannot pay her Kesuvah. The Rif (Teshuvah 14) brings a proof from Kesuvos 51a. One may divorce a sick wife only if he gives her Kesuvah. If the husband does not accept the law, we excommunicate him.

Rebuttal (Bedek ha'Bayis): We do not rely on this. No famous Poskim allude to this. It is easy to dispel the proof. Many Teshuvos are mistakenly attributed to Gedolim. See the Rivash (91) and Rosh (42:1, brought in Beis Yosef Sof Siman 1 DH Nosei and Sof Siman 117 DH Kosav. A woman cannot refuse to be divorced without receiving her Kesuvah first. Even after R. Gershom's decree, she is divorced. She claims her Kesuvah like a normal debt (Rosh).)

Chelkas Mechokek (5): The Rosh discusses an epilectic, which is a great Mum. He could agree that one who opts to divorce without compelling reason must pay the Kesuvah first.

Defense (Chasam Sofer Sof Gitin DH R. Akiva): All the Acharonim agree with the Rashba. The Yerushalmi says that Beis Shamai obligate Kinuy (warning one's wife against seclusion), i.e. when he sees immodesty, for they forbid divorcing without witnesses of immorality. Tosfos (Sotah 3a DH Rebbi) asks that R. Akiva also obligates Kinuy, even though he permits one who found a nicer woman to divorce! Like the Rashba, we can say that Kinuy is obligatory when he cannot pay her Kesuvah. Beis Hillel say that Kinuy is optional. This is like the opinion that Chachamim enacted Kesuvah lest it be light in his eyes to divorce her. According to the opinion that it is mid'Oraisa, he can divorce and owe the money. R. Nosan Adler says that Beis Shamai must hold that Kesuvah is mid'Oraisa. Since they require witnesses of immorality to divorce, it is not light in his eyes to divorce her!

Beis Yosef (DH v'Chosav ha'Rashba, citing the Rashba 4:186): If one married in a place where we divorce only with her consent, it is as if she explicitly married him on this condition. If he transgresses this, he gets the normal punishment, be it a fine or excommunication. This is even if they moved to a place where men divorce b'Al Korchah.

Rema: This is letter of the law. R. Gershom imposed a Cherem against divorcing b'Al Korchah, unless she was Overes Al Das (caused him to transgress or acted immodestly). If he divorced her b'Al Korchah and she remarried, her ex-husband is no longer called a transgressor. If he divorced her willingly and the Get was found to be Pasul, he may divorce her again b'Al Korchah. Some say that for a Mitzvah he may divorce her b'Al Korchah or marry two women.

Mordechai (6:55): A Cherem of R. Gershom forbids having two wives. To marry another woman, he divorces his first wife and pays her Kesuvah.

Darchei Moshe (1): When it is proper to divorce (e.g. Zivug Sheni and he hates her - Beis Shmuel 6), she must accept the Get even if he cannot pay the Kesuvah. The SMaK (184) and Rosh (42:1) connote that R. Gershom's decree applies even if he is ready to pay the Kesuvah, unless there are witnesses of Overes Al Das. However, the Mordechai connotes otherwise.

Noda bi'Yehudah (1 EH 84 b'Sof): Chachamim did not enact Kesuvah for a Chereshes, lest men refrain from marrying her. Being unable to divorce her b'Al Korchah is a greater burden than a Kesuvah. Perhaps R. Gershom did not decree about a Chereshes for this reason! However, we cannot be lenient if the Rishonim did not specify. A Safek Cherem is forbidden mid'Oraisa.

R. Akiva Eiger: R. Gershom's enactment was to help her. A Chereshes' gestures do not indicate desire, but (also they do not indicate opposition, so) we cannot say that she is being divorced by force.

Beis Shmuel (12): If R. Gershom's decree is like an enactment of Chazal, if one divorced b'Al Korchah, even b'Di'eved she is not divorced.

Pischei Teshuvah (7): The Rema says that b'Di'eved she is divorced. All agree that divorce of a Shoteh works b'Di'eved, for he cannot remarry her. All the Rishonim rule like Rava, who says that transgressing (any Lav) does not help. Tosfos (Temurah 6a DH v'Hashta) does not apply this to one who swore not to divorce, for he invented the Lav. One who transgressed R. Gershom's Cherem did not invent the Isur, so we should obligate him to remarry her! Until she remarries, he transgresses every day! Get Pashut (24) says that b'Di'eved, the Get did not help. Perhaps he means that it is Safek Gerushin. Mahari Mintz says that the Get did not work. Noda bi'Yehudah (2: EH 129 ume'Atah) suggests that perhaps he means that it did not exempt him of his monetary obligations to her. Alternatively, if the scribe knew that he wanted to divorce b'Al Korchah, (if Shelichus is required to write a Get), it is Pasul, for there is no Shelichus for Aveiros. If the witnesses knew, they are Pesulim.