Answer: Just about any garden crop can be grown here successfully, except rhubarb (not cold enough). Growers are constantly developing new varieties, so sometimes old favorites disappear. Rather than specific varieties, try to find those that mature in as few days as possible (so they don't have to endure the summer heat as long, for example), and are tolerant of heat. Varieties with "early" or "heat" in the names are a clue. Also, choose smaller fruit sizes, which are less prone to water stress and cracking. For example, the small or mid-size tomatoes I list below do well here, whereas the big "beefsteaks" do not.
Beans: Early Bush Italian, Blue Lake
Tomatoes: Heatwave, Celebrity, cherry, yellow pear
Cucumbers: large cukes can get bitter when the heat hits, so go for smaller size, such as the Double Feature Hybrid. Also, Armenium cukes do fairly well.
Zucchini: any; Sweet Zuke Hybrid, Roly Poly, scallop (Peter Pan), crookneck (Pic-n-Pic)
Squash: spaghetti; butternut
Peppers: just about any chili pepper will grow here; for bells, try Early Crisp
Lettuces: any leaf lettuces do extremely well; head lettuces don't form very well. Also, other greens, such as chard, kale, mustard, collard do very well.
Cabbage: smaller head cabbage, bok choy, chinese cabbage
Carrots: If you have clay soil, choose a shorter carrot, such as Short 'n Sweet.
Radishes: just about any because they mature so quickly
Corn: Sweet Bantam
More important that the variety is the timing of when you plant. Be aware that there are two distinct growing seasons in the low desert with different annual vegetables thriving in each season. (In other words, you couldn't plant all of the veggies on your list at the same time and have them thrive.) There's a cool season from approximately the end of September through April. Annuals can be installed from September to February. The warm season starts with planting in mid to late February. Some plants will make it through the summer's heat; others will end their growth when the heat arrives. A good reference book that contains planting calendars for the low desert is called "Desert Gardening for Beginners: How to Grow Vegetables, Flowers and Herbs in an Arid Climate." ISBN 0-9651987-2-3. Good luck!
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