arXiv subjects
Publications and source records attributed to Stanislaw Betley.
We model the field $F_1$ of one element as a lambda ring $\bf Z$ with the canonical lambda structure. We show that then we can calculate the Riemann zeta function of integers in two ways: the first, geometrical, as a zeta function of the affine line over $F_1$ and the second, categorical, as a zeta function of the category of modules over $F_1$.
The paper is devoted to study the space of multiplicative maps from the Eilenberg-MacLane spectrum $H\Z$ to an arbitrary ring spectrum $R$. We try to generalize the approach of Schwede from "Formal groups and stable homotopy of commutative rings", where the special case of the mentioned above problem was solved in full generality. Among other results we propose a definition of a formal group law in any ring spectrum, which might be of interest in its own.
The paper gives an answer to the question whether the Galois, separable or etale extension of an Eilenberg-MacLane spectrum in the category of ring spectra is again an Eilenberg-MacLane spectrum. We get a full answer in the Galois case. The question in separable and etale cases is answered only under additional hypothesis.