Among the most famous hagiographies of Adi Shankara is the Madhaviya Shankara Vijaya. This work has significant importance in advaita tradition.
https://www.advaita-vedanta.org/avhp/sankara-vijayam.html
mAdhavIya Sankaravijaya - The mAdhavIya is probably the oldest available, and also the most authentic and widely known among the different Sankaravijayas today. It is certainly the most popular such text in the advaita tradition, and is also known as the sam.kshepa Sankarajaya. The popularity of this work derives from the fame of its author, mAdhava, who is usually identified with vidyAraNya, the 14th century maThAdhipati at Sringeri.
The Sanskrit version of this work can be found at -
https://archive.org/details/Shankara.Digvijaya.Satika
A slightly sanitized translation by Swami Tapasyananda (we will see why sanitization is done) is found at -
https://www.amazon.in/Sankara-Digvijaya-Swami-Tapasyananda-ebook/dp/B00BUV1H3W
According to the madhaviya shankara vijaya, Kumarila, the mimamsa scholar, is an incarnation of Skanda (son of Shiva) and Adi Shankara himself is an incarnation of Shiva. This is mentioned in first chapter.
According to the first chapter of this work (1.60-1.98), there was a king by name Sudhanvan (incarnation of Indra) who was a Buddhist. Kumarila arrives at the king's place, has arguments with Buddhists and defeats them. The king's belief in vedic dharma is established. At the instigation of Kumarila, the king orders his minions to kill all buddhists, including children and elderly, right from Rameswaram to the Himalayas. (This part is sanitized in the translation by the Swami). Some of the relevant Sanskrit text is given below -
Note the vrddhabAlakam at the end of first line. Every Buddhist right from children to elderly was killed. This perfectly fits the definition of genocide.
Here the translation continues -
He also threatened with dire punishment those officers who showed any hesitation in carrying out this order, however close he might be to him. Indeed; powetful rulers eliminate even friends and relatives, if they tum disobedient or hostile. Did not Parasurama kill his mother under such circumstances?
Thus, the text seems to be justifying the genocide of non-believers (Buddhists).
Adi Shankara himself does not seem to have any qualms in associating himself with this king. For the king was allowed to accompany Shankara during his tour of the country -
The king helps Adi Shankara in his tour by helping him defeat the kapalikas (another slaughter of kapalikas this time, but at least the kapalikas supposedly brought it on themselves as they were allegedly violent).
My question here is not whether these events are real. They may have been made up, exaggerated or blown out of proportion or partly real or who knows what. However, we see two stanuch followers of the vedas - (Kumarila and Adi Shankara focused on karma and jnana kandas of vedas respectively) - one instigating a king to commit genocide and other having no qualms in associating with such a king, according to this hagiography which is very popular in advaita circles.
If these staunch followers of vedas did not see anything wrong in the genocide of Buddhists (as per this Shankara vijaya), the natural question that arises is
whether the vedas and/or smritis themselves sanction genocide of non-believers like Buddhists? Is genocide of non-believers permitted according to Hindu texts?
Comment
Since one of the answers says that the madhaviya shankara digvijaya is not an important one: On the mAdhavIya Shankara Digvijaya's popularity, I have only quoted the website of advaita-vedanta.org. Another indicator of its popularity is its translation into local languages and distribution by Sringeri matha. Even the Sringeri matha website regards this work as very popular and widely accepted, most authentic -
The Madhaviya Shankara Vijayam, the most popular and widely accepted account of Sri Adi Shankara’s life, describes the advent of Sri Adi Shankara thus..
https://www.sringeri.net/history/sri-adi-shankaracharya/biography
The Madhaviya is the the most authentic and widely known among the different Sankaravijayas today. It is certainly the most popular such text in the Advaita tradition, and is also known as the Samkshepa Sankarajaya. The popularity of this work derives from the fame of its author, Madhava, who is actually Jagadguru Sri Vidyaranya, the 12th Acharya of the Sriingeri Sharada Peetham.