Ants on Shabbat! What can be done?

The Shabbat meal is over and you've just finished clearing the table. Picking up the broom, you start to sweep the living room... only to discover a parade of ants marching across the floor. Are you allowed to sweep them away?

The answer is yes, even if the ants aren't mingled with dust and  dirt. According to both Sephardic and Ashkenazi authorities, one may sweep the ants away.

But what about ant spray -- may it be used on Shabbat?

One may not spray directly on the ants as that would be killing them. However, one may prevent them from reaching certain areas, such as countertops or cabinets, by spraying those areas before the ants get there.

In summary: According to both Ashkenazi and Sephardic authorities, it is permissible to sweep ants away. (The halachah is different for other creepy-crawlies.)

Spraying directly on the ants is prohibited, but spraying in places where they haven't yet reached is permitted.