An Alternative to Spherical Witt Vectors

We give a direct construction of the ring spectrum of spherical Witt vectors of a perfect Fₚ-algebra R as the completion of the spherical monoid algebra S[R] of the multiplicative monoid (R,·) at the ideal I = fib(S[R] → R). This generalizes a construction of Cuntz and Deninger. We also use this to give a description of the category of p-complete modules over the spherical Witt vectors and a universal property for spherical Witt vectors as an E₁-ring.