Where does the symbol $\mathcal O$ for sheaves come from?

Question

Sheafs are often denoted by the letter $\mathcal O$. What does this O stand for? To me it seems that more natural choices of symbols for sheaves would be $\mathcal S$ or $\mathcal F$ (for the french faisceau).

Answer 1

Quoting the historical footnote in Grauert/Remmert, Coherent Analytic Sheaves, concerning the origin of the notation $\mathcal{O}$ for the rings of holomorphic functions (and their associated sheaves):

Some people think the symbol $\mathcal{O}$ was chosen in honor of Oka, sometimes it is even said that $\mathcal{O}$ reflects the French pronunciation of holomorphe. The truth is that the symbol was chosen accidentally. In a letter to the authors from March 22, 1982, H. Cartan writes: "Je m'étais simplement inspiré d'une notation utilisée par van der Waerden dans son classique traité 'Moderne Algebra' (cf. par exemple §16 de la 2e édition allemande, p.52)"