We present 1.3 millimeter ALMA Cycle 0 observations of the edge-on debris disk around the nearby, ~10 Myr-old, M-type star AU Mic. These observations obtain 0.6 arcsec (6 AU) resolution and reveal two distinct emission components: (1) the previously known dust belt that extends to a radius of 40 AU, and (2) a newly recognized central peak that remains unresolved. The cold dust belt of mass about 1 lunar mass is resolved in the radial direction with a rising emission profile that peaks sharply at the location of the outer edge of the birth ring of planetesimals hypothesized to explain the midplane scattered light gradients. No significant asymmetries are discerned in the structure or position of this dust belt. The central peak identified in the ALMA image is ~6 times brighter than the stellar photosphere, which indicates an additional emission process in the inner regions of the system. Emission from a stellar corona or activity may contribute, but the observations show no signs of temporal variations characteristic of radio-wave flares. We suggest that this central component may be dominated by dust emission from an inner planetesimal belt of mass about 0.01 lunar mass, consistent with a lack of emission shortward of 25 microns and a location <3 AU from the star. Future millimeter observations can test this assertion, as an inner dust belt should be readily separated from the central star at higher angular resolution.
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