write up

Short definition from Wiktionary

Verb

1. 1
   Used other than figuratively or idiomatically: see write, up.
2. 2
   To produce by writing.
3. 3
   To document officially the faults, offenses, or wrongdoing of.
4. 4
   To write about positively; to praise in writing.
5. 5
   To make an upward adjustment in the value of an asset.
6. 6
   To annotate a stamp album page with details about the stamp, such as die used or colour variety.

Noun

1. 1
   A written account of something, as a record.
2. 2
   An increase made to the book value of an asset that was previously undervalued.
3. 3
   A review published in the print or online media for a film, book, etc.