"Seeking a piece of history to start my collection."
"Search for a remnant that the merchant would be proud to add to their collection."
Quest-Giver Dialogue 
"I want to start a collection that chronicles the history of Fódlan, but I'm having trouble getting my hands on anything significant. Honestly, it might be easier to excavate an artifact rather than trying to find one for sale..."
Quest Completion Dialogue
"Ah, magnificent! Exactly what I was looking for. Clearly I asked the right person for help."
Given to you by a merchant in the marketplace.
- Gemstone Beads x1
- Ancient Coin x1
- 500 Renown
Subjective: The following part of this article is based upon the editor's personal experiences and opinions, and therefore may not be applicable for all readers.
Talk to the merchant in the marketplace and accept the quest on the player's next day off. Head to the cathedral and find the "Cornerstone Fragment". Give it to the merchant to complete the quest.