Voters next month will be asked to authorize funding for roof repairs at four Pembroke schools. The Massachusetts School Building Authority has agreed to reimburse the town for 50 to 55 percent of the cost of the work, which would be done at the Hobomock and North Pembroke elementary schools, the Community Middle School, and the High School. The Special Town Meeting that convenes Nov. 12 will consider authorizing the full project budget – currently estimated at $10.6 million. Approval would be subject to passage of a debt exclusion, or temporary tax increase, to cover the town’s share, at a special election that has not yet been set. The exact percentage of the state’s reimbursement would be set next January. School officials say all four schools underwent extensive renovations over the past decade, but the projects did not involve replacing the roofs, some of whose sections are 20 to 30 years old.