1. A multiprocessor computer system comprising: main memory; a remote processor capable of accessing said main memory; a remote cache device operative to store accesses by said remote processor to said main memory; a filter tag cache device associated with said main memory, said filter cache device being operative to store information relating to remote ownership of data in said main memory including ownership by said remote processor, said filter cache device being operative to selectively invalidate filter tag cache entries when space is required in said filter tag cache device for new cache entries; wherein said remote cache device is responsive to events indicating that a cache entry has low value to said remote processor to send a hint to said filter tag cache device; and wherein said filter tag cache device is responsive to receipt of a said hint in selecting a filter tag cache entry to invalidate.