Provided is a polymer capable of providing a coating film that has good initial adhesiveness to a base material and good adhesiveness thereto after a pressure cooker test, and has excellent abrasion resistance as determined by a falling sand abrasion test. The polymer includes a perhaloolefin unit, a vinyl ester unit that contains neither a hydroxy group nor an aromatic ring; and a hydroxy group-containing monomer unit. The polymer has a hydroxyl value of 110 mgKOH/g or greater.