2025/08/17 by Riedel, Florian
#55P43 #Algebraic Topology (math.AT) #FOS: Mathematics
paper · doi:10.48550/arxiv.2508.12462
We investigate whether an arbitrary non-zero 𝔼_∞-ring A admits a reduced point, meaning an 𝔼_∞-map A→ T such that π∗T is a graded field. We show that if 2∈ π0A is not invertible, then A admits a reduced point and as an application deduce that a free A-module on n generators cannot be built from n-1 many cells. Perhaps surprisingly, the existence of reduced points completely fails at odd primes. More precisely, for any prime p>2, we construct a non-zero 𝔼_∞-ring over \mathbbFp which admits no map to an 𝔼2-algebra T such that π0T is a field.