According to the Samaritan Pentateuch, Mt. Gerizim is the place where Hashem would like his Temple constructed. No temple currently stands on Mt. Gerizim.
The reasons (political and theological) that no Jewish temple has been built in Jerusalem in modern days under Rabbinic Judaism are well known.
Why have Samaritans not built (or rebuilt) a temple at Mt. Gerizim? Is the delay is more practical in nature (e.g. lack of funds, lack of architectural skills, refusal of building permits, fear of sectarian violence, or simple apathy) or are they delaying the construction for doctrinal reasons (e.g. waiting for Messiah, waiting for a certain sign in the heavens, etc.).