Sharding is planned for Ethereum 2.0, which will split the state into a few hundred shards, connected along a hypercube network topology.
Does each shard have its own address space, or, is there a global address space?
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There is a shard ID for each shard that is a prefix to the address. For details, see https://ethresear.ch/t/minimal-sharding-protocol-extension/1823 and https://github.com/Drops-of-Diamond/diamond_drops/issues/13 for updates.