Writing the screenplay will be Steven Knight. Vertigo is based on a french book titled D'entre les morts (lit. '"From Among the Dead"') authored by Boileau-Narcejac (the pen name for writing partners Pierrer Bolieau and Pierre Ayraud). The English translation is called "The living and the Dead."
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The 1954 film adaptation starred James Steward as John "Scottie" Ferguson.
Here is the goodreads synopsis of The Living and the Dead:
Flavieres was not a man to be surprised by little slips of human contact. So when his old friend Paul Gevigne said 'I want you to keep an eye on my wife.' Flavieres thought the reasons were pretty obvious.
He was wrong.
Terribly wrong.
Source: Variety.com