If the ashes are from wood or lump charcoal (as opposed to briquettes) I add them to my mulch pile. As the OP noted, wood ash is typically alkaline.
Wood Ash: An Alternative Liming Material for Agricultural Soils
"Wood Ash and Agricultural Lime
Calcitic limestone (CaCO3) is the liming material used most often to neutralize acid soils. Burned lime (quick lime, calcium oxide or CaO) and hydrated lime (slaked lime, builder's lime, calcium hydroxide or Ca(OH)2) are also used for soil application in Europe; however, the higher cost of these materials limits their use in western Canada. Wood ash contains oxides and hydroxides of calcium, magnesium, potassium and, to a lesser extent, sodium making wood ash similar to burned or hydrated lime in its mode of action.
Wood ash also contains many of the nutrients originally absorbed from the soil by tree growth, so it may improve crop growth through improved nutrition. By comparison, agricultural lime contains only minimal amounts of plant nutrients. A significant amount of phosphorus, calcium, magnesium and potassium (potash) is added to the soil when wood ash is used as a liming material. "