The Gemara discusses the obligation of burial (kevurah) and debates whether burial is a Torah obligation or a rabbinic one, deriving from 'ki kavor tikberenu' (you shall surely bury him). This establishes the halachic foundation for why cremation is prohibited — it violates the positive commandment of burial.
אִיבַּעְיָא לְהוּ: קְבוּרָה מִשּׁוּם בִּזְיוֹנָא הוּא, אוֹ מִשּׁוּם כַּפָּרָה הוּא? לְמַאי נָפְקָא מִינַּהּ? דְּאָמַר: לָא בָּעֵינָא דְּלִיקְבְּרוּהּ לְהָהוּא גַּבְרָא. אִי אָמְרַתְּ מִשּׁוּם בִּזְיוֹנָא הוּא – לָא כֹּל כְּמִינֵּיהּ, וְאִי אָמְרַתְּ מִשּׁוּם כַּפָּרָה הוּא – הָא אָמַר: לָא בָּעֵינָא כַּפָּרָה. מַאי?
§ A dilemma was raised before the Sages: Is burial obligatory on account of disgrace, i.e., so that the deceased should not suffer the disgrace of being left exposed as his body begins to decompose, or is it on account of atonement, i.e., so that the deceased will achieve atonement by being returned to the ground from which he was formed? The Gemara asks: What is the practical difference that arises from knowing the reason that burial is necessary? The Gemara answers: There is a difference in a case where one said before he died: I do not want them to bury that man, i.e., myself. If you say that burial is required on account of disgrace, it is not in his power to waive his own burial, as his family shares in the disgrace. But if you say that burial is required on account of atonement, didn’t he effectively say: I do not want atonement, and with regard to himself one should be able to do as he wishes? What, then, is the halakha?