wood ash is alkaline, and provides other nutrients, but it takes more of it than lime, and can damage seedlings.

From http://www.ext.vt.edu/pubs/envirohort/426-313/426-313.html

"You can use wood ashes as a soil amendment. They contain potash (potassium), phosphate, boron, and other elements. Wood ashes also raise the soil pH; but you must use twice as much ash as limestone for the same effect. Ashes should not come into contact with germinating seedlings or plant roots as they may cause root burn. Spread in a thin layer over the winter, and incorporate it into the soil; check the pH yearly if you use wood ashes. Never use coal ashes or large amounts of wood ash (no more than 20 pounds per 1,000 square feet), as toxicity problems may occur. "



Haven't grown potatoes, but googled the question and found many suggestions. Since they are also a nightshade, keep them away from tomatoes and egg-plant.