STAR NYS Tax relief

Full-time resident of New York City.   I live in a Co-op apartment that I own. 

Our applicable share of real estate property taxes are derived by the Co-Op tax accountant. 

Once a year I receive a monthly maintenance bill with a line item indicating "STAR" and an associated dollar amount.  And, another line item "ABATEMENT" with an associated dollar amount. 

I do NOT itemize taxes on my Federal and New York State return. 

Do I need to reduce my real estate property tax dollar amount by the dollar amount of the STAR I received?

Also, do I need to reduce my property tax dollar amount by the dollar amount of the ABATEMENT I received?

I am a but confused, because while doing my NYS return, with TurboTax, I thought I read am info blurb that read that I do not have to deduct my property tax paid if I do NOT itemize - but maybe I am misinterpreting.