Fasting is obligatory in (the month of) Ramadan Sahih al-Bukhari 1892
Arabic hadith text
حَدَّثَنَا مُسَدَّدٌ، حَدَّثَنَا إِسْمَاعِيلُ، عَنْ أَيُّوبَ، عَنْ نَافِعٍ، عَنِ ابْنِ عُمَرَ ـ رضى الله عنهما ـ قَالَصَامَ النَّبِيُّ صلى الله عليه وسلم عَاشُورَاءَ، وَأَمَرَ بِصِيَامِهِ. فَلَمَّا فُرِضَ رَمَضَانُ تُرِكَ.وَكَانَ عَبْدُ اللَّهِ لاَ يَصُومُهُ، إِلاَّ أَنْ يُوَافِقَ صَوْمَهُ
Translation
Narrated Ibn `Umar
The Prophet (ﷺ) observed the fast on the 10th of Muharram ('Ashura), and ordered (Muslims) to fast on that day, but when the fasting of the month of Ramadan was prescribed, the fasting of the 'Ashura' was abandoned. `Abdullah did not use to fast on that day unless it coincided with his routine fasting by chance.