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May 13, 2018 at 13:18 comment added Mohan About 3), I thought any non-trivial line bundle in $Pic^0$ gave a rank one MCM module over the cone over an abelian surface thanks to Kodaira vanishing.
Nov 28, 2009 at 20:36 comment added Kevin Buzzard Thanks for your comments. I'm the OP (I posted under a temporary ID). I'm now mainly interested in the case where A is a power series ring in several variables over a characteristic zero field.
Nov 28, 2009 at 19:24 history edited Hailong Dao CC BY-SA 2.5
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Nov 28, 2009 at 19:16 history answered Hailong Dao CC BY-SA 2.5