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The Paris Agreement states that, relative to pre-industrial times, the increase in global average temperature should be kept to well below 2 A degrees C and efforts should be made to limit the temperature increase to 1.5 A degrees C. Emissions scenarios consistent with these targets are derived. For an eventual 2 A degrees C warming target, this could be achieved even if CO2 emissions remained positive. For a 1.5 A degrees C target, CO2 emissions could remain positive, but only if a substantial and long-lasting temperature overshoot is accepted. In both cases, a warming overshoot of 0.2 to 0.4 A degrees C appears unavoidable. If the allowable (or unavoidable) overshoot is small, then negative emissions are almost certainly required for the 1.5 A degrees C target, peaking at negative 1.3 GtC/year. In this scenario, temperature stabilization occurs, but cumulative emissions continue to increase, contrary to a common belief regarding the relationship between temperature and cumulative emissions. Changes to the Paris Agreement to accommodate the overshoot possibility are suggested. For sea level rise, tipping points that might lead to inevitable collapse of Antarctic ice sheets or shelves might be avoided for the 2 A degrees C target (for major ice shelves) or for the 1.5 A degrees C target for the West Antarctic Ice Sheet. Even with the 1.5 A degrees C target, however, sea level will continue to rise at a substantial rate for centuries.