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21
votes
1answer
1k views

What is known about the sum x^{n^2}/n?

It follows from a general theorem of Honda that the formal group with the logarithm $$ x+x^{2^s}/2+x^{3^s}/3+x^{4^s}/4+\cdots $$ has integer coefficients. I became interested in it because its ...
20
votes
3answers
1k views

Modern Source for Spectra (including Ring Spectra)

I am looking for a modern introduction to Spectra that improves on the treatment by Adams in his "Stable Homotopy and Generalized Homology" notes (by improves I mean taking into account what has been ...
22
votes
4answers
2k views

What is a simplicial commutative ring from the point of view of homotopy theory?

Let $k$ be a field. There are two natural categories to consider: The category of simplicial commutative $k$-algebras. The category of connective $E_\infty$ $k$-algebras (i.e., chain complexes of ...
7
votes
2answers
412 views

Absence of Maps Between p-local and q-local spectra

Suppose $X$ and $Y$ are spectra (or homotopy classes thereof) such that $X$ is p-local and $Y$ is q-local, for primes $p\neq q$. Is it indeed true then, and if so how would one show that ...