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Dec 10, 2013 at 13:33 comment added user42721 Just a remark : your property (1) i.e $Mon^0 = MT^{der}$ does not characterise Shimura subvarieties at all - indeed it holds for any subvariety of $A_{g,m}$ provided it contains a CM point. (I am assuming, by $Mon^0$ you mean the neutral component of the Zariski closure of the monodromy representation attached to the smooth locus of your subvariety)
Oct 2, 2013 at 12:11 history asked Darius Math CC BY-SA 3.0