Pope Lucius has disputed with the Holy Roman Emperor Frederick I over the disposal of the territories of the late Countess Matilda of Tuscany.

The controversy over the succession to the inheritance of the Countess had been left unsettled by an agreement of 1177, and the Emperor had proposed in 1182 that the Curia should renounce its claim, receiving in exchange two-tenths of the imperial income from Italy, one-tenth for the Pope and the other tenth for the cardinals.

Lucius had consented neither to this proposition nor to another compromise suggested by Frederick I the next year, nor does a personal discussion between the two potentates at Verona in October 1184 lead to any definite result.

In the meantime, other causes of disagreement had appeared when the Pope refused to comply with Frederick I's wishes as to the regulation of German episcopal elections which had taken place during the schism, especially as regards a contested election to the See of Treves in 1183.

During the conflict between Frederick I and the papacy, the problem of heresy requires a political solution.

In November 1184, Pope Lucius III, aiming to abolish completely Christian heresy, decrees in Ad abolendam that all "counts, barons, rectors, [and] consuls of cities and other places" who do not join in the struggle against heresy when called upon to do so will be excommunicated and their territories placed under interdict—and declares that these provisions join the apostolic authority of the church with the sanction of imperial power.

Among the particular sects mentioned in Ad abolendam are the Cathars, Humiliati, Waldensians, Arnoldists, and Josephines.

More important than the direct attack on heresy, however, is the stipulation of equal measures for those who support heretics, overtly or indirectly.

Those accused of heresy, if they cannot prove their innocence or forswear their errors, or if they backslide into error subsequently, are to be handed over to the lay authorities to receive their animadversio debita ("due penalty").

All those who support heresy are to be deprived of their many rights: the right to hold public office, the right to trial, the right to draft a will, and the hereditability of their fiefs and offices.

For the enforcement of the measures demanded by the decretal, Lucius obligates all patriarchs, archbishops, and bishops to re-announce the excommunication on certain feasts and holidays.

Those who do not observe this for three years consecutively are to be deprived of their ecclesiastical offices.

The bishops are furthermore obligated to "seek out" heretics.

They are to make bi- or triannual rounds of their dioceses, visiting locations of suspicion and question the people about the existence of heresy.

The people will be required to swear under oath (compurgation) anything they know about heretical activity.

All oath-breakers are to be treated as heretics.

Though largely ineffective, the document serves as tinder for the eventual flames of the Albigensian Crusade and the Inquisitions.

Contrary to what is often said, Pope Lucius did not institute the Inquisition, which will not be created until the reign of Pope Gregory IX in 1234.