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Sandbox

Every wiki needs a sandbox! Just test between the horizontal rules below (*** in the source) and otherwise don't worry about messing things up.


localize at p complete to ring p localize at p complete to field complete to field complete in absolute-value metric complete in p-adic metric p algebraic completion algebraic completion algebraic completion complete in absolute-value metric ¯ p¯ complete in p-adic metric p \array { & & \mathbb{N} & \overset{\text{localize at }\,p}\rightarrow \\ & & \text{complete to ring}\downarrow & & \mathbb{Z}_p \\ & & \mathbb{Z} & \overset{\text{localize at }\,p}\rightarrow \\ & & \text{complete to field}\downarrow & & \text{complete to field}\downarrow \\ \mathbb{R} & \overset{\text{complete in absolute-value metric}}\leftarrow & \mathbb{Q} & \overset{\text{complete in }\,p\text{-adic metric}}\rightarrow & \mathbb{Q}_p \\ \text{algebraic completion}\downarrow & & \text{algebraic completion}\downarrow & & \text{algebraic completion}\downarrow \\ \mathbb{C} & \overset{\text{complete in absolute-value metric}}\leftarrow & \bar{\mathbb{Q}} & & \overline{\mathbb{Q}_p} & \overset{\text{complete in }\,p\text{-adic metric}}\rightarrow & \mathbb{C}_p }

category: meta

Revised on June 20, 2014 13:14:01 by Toby Bartels (98.16.175.187)