If you live in the Sarasota County school district, it looks like your taxes are headed up. Right now, it looks like the millage increase required by state law for next school year will go up by just over a quarter mill. Board members were told yesterday the amount is not something they control. “The required local effort will be raised by the governor’s office,” according to board Chairwoman Caroline Zucker. With the possible millage increase, the owner of a home assessed at $100,000 would pay about $790.60 in district taxes.