write down

verb4

1. •
   To produce or set (something) down in writing; to record something.
2. •
   To make a downward adjustment in the value of an asset.
3. •
   To write (something) in a simple or condescending style.

   • Good heavens, I can't write down to the level of the vulgar public! — 2011
4. •
   To condemn in writing; to document the faults, offenses, or wrongdoing of.