Composition for forming resist underlayer film having saccharin skeleton

A polymer having a unit structure represented by formula (1) below:

• in formula (1), Ar represents a benzene ring, a naphthalene ring, or an anthracene ring,
• R1 represents a hydroxy group, a mercapto group which may be protected by a methyl group, an amino group which may be protected by a methyl group, a halogen atom, or an alkyl group having 1 to 10 carbon atoms, which may be substituted or interrupted by a hetero atom or may be substituted by a hydroxy group,
• n1 represents an integer of 0 to 3,
• n2 represents 1 or 2,
• L1 represents a single bond or an alkylene group having 1 to 10 carbon atoms,
• Y represents a group represented by formula (A-2) below,
• T1 represents a single bond, an ether bond, an ester bond, or an amide bond (—NHCO—) when n2 is 1,
• T1 represents a nitrogen atom or an amide bond when n2 is 2,
• in formula (A-2), T2 represents a divalent organic group having 1 to 10 carbon atoms,
• X represents —CO— or —SO2—,
• Ra represents a halogen atom, an alkyl group having 1 to 8 carbon atoms, which may have a substituent, an alkoxy group having 1 to 8 carbon atoms, which may have a substituent, an alkylthio group having 1 to 5 carbon atoms, a nitro group, or a cyano group,
• n represents an integer of 0 to 4,
• when there are two or more Ra's, two or more Ra's may be identical or different, and
• * represents a bond.