An Alternative to Spherical Witt Vectors

2024/05/15 by Nikolaus, Thomas, Yakerson, Maria
#Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #Commutative Algebra (math.AC) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2405.09606

Abstract

We give a direct construction of the ring spectrum of spherical Witt vectors of a perfect \mathbbF_p-algebra R as the completion of the spherical monoid algebra \mathbbS[R] of the multiplicative monoid (R,⋅) at the ideal I = fib(\mathbbS[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.

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