Each core has its own set of registers, MMU, TLB, level 1 caches (data and instructions), level 2 cache (this depends on the processor), etc. Cache coherency is maintained through the core via "QPI", and in the case of high-performance Core 7 and server processors such as Xeon, Cache Coherency is supported on processors on a multiprocessor motherboard, exposing "QPI" to the external contacts of these processors (for processors where multiprocessor cache coherency not supported, "QPI" is not "displayed").
Wiki article: Nehalem
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