According to the present invention, a polymer is obtained by polycondensation of a fluorinated dicarboxylic acid derivative of the general formula (M-1) or an acid anhydride of the fluorinated dicarboxylic acid with a polyfunctional compound having two to four reactive groups corresponding in reactivity to carbonyl moieties of the fluorinated dicarboxylic acid derivative or acid anhydride. [Chem. 134] AOCF2C-Q-CF2COA′  (M-1) In the above formula, Q represents a divalent organic group having a substituted or unsubstituted aromatic ring; and A and A′ each independently represent an organic group. This polymer exhibits a sufficiently low dielectric constant for use as a semiconductor protection film and has the capability of forming a film at a relatively low temperature of 250° C. or lower.