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Let O be the ring of integers of a number field K. For an O-algebra R which is torsion free as an O-module we define what we mean by a Lambda_O-ring structure on R. We can determine whether a finite etale K-algebra E with Lambda_O-ring structure has an integral model in terms of a Deligne-Ribet monoid of K. This a commutative monoid whose invertible elements form a ray class group.
We develop algorithms to turn quotients of rings of rings of integers into effective Euclidean rings by giving polynomial algorithms for all fundamental ring operations. In addition, we study normal forms for modules over such rings and their behavio
Let $K$ be a number field with ring of integers $R$. Given a modulus $mathfrak{m}$ for $K$ and a group $Gamma$ of residues modulo $mathfrak{m}$, we consider the semi-direct product $Rrtimes R_{mathfrak{m},Gamma}$ obtained by restricting the multiplic
We consider generalized $Lambda$-structures on algebras and schemes over the ring of integers $mathit{O}_K$ of a number field $K$. When $K=mathbb{Q}$, these agree with the $lambda$-ring structures of algebraic K-theory. We then study reduced finite f
A set $mathcal{A}$ is said to be an additive $h$-basis if each element in ${0,1,ldots,hn}$ can be written as an $h$-sum of elements of $mathcal{A}$ in {it at least} one way. We seek multiple representations as $h$-sums, and, in this paper we make a s
We determine higher topological Hochschild homology of rings of integers in number fields with coefficients in suitable residue fields. We use the iterative description of higher THH for this and Postnikov arguments that allow us to reduce the necess