Bring a large pot of water to a boil, salt it, add the pasta and cook until al dente. Drain, reserving a ladleful of the pasta cooking water.
While the pasta is working, in a large skillet, heat the EVOO, 2 turns of the pan, over medium-high heat. Add the corn, bell pepper, shallots and garlic and cook for 5 minutes, then add the peas and cook for 1 minute; season with salt and pepper. Stir in the tomatoes and toss. Stir in the crab, butter and Old Bay seasoning, then stir in the reserved pasta cooking water. Add the pasta and tarragon and toss.