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I started a PhD in chromatic homotopy three years ago, but I had to quit it due to personal reasons after one year. Last week I was looking at all my notes from that period and I was wondering where a …

There is a theorem by Hopkins and Smith which states that for every $n > 0$ there is an ideal $I_n = (v_0^{k_0}, \dots, v_n^{k_n})$ such that there exist a spectrum $X_n$ with the following homology: …

I have a countable sequence of finite suspension spectra $X_i$, whose $BP$-homology is a $BP_*(BP)$-comodule. Let's assume $BP_*(X_i) = \Sigma^{d_i} BP_* / (v_0^{k_0}, \dots v_i^{k_i}),$ for some $d_n …

Let $X$ be a suspension spectra whose $BP$-homology is infinitely generated ($BP_*(X) = \Sigma^d BP_*/I$, where $I$ has the form $I=(v_0^{i_0}, \dots , v_n^{i_n})$ such that the homology is a $BP_*(BP …

QUESTION EDITED: There was a mistake, the spectrum i had written before didn't even exist, so a big thanks to the people who made me notice that in the comments. Let $X_n$ be the spectrum such that $ …

There are some criteria which tell us when a spectrum $X$ is chromatically complete (it's the homotopy limit of its chromatic tower): It has to be p-local and finite, according to the chromatic conv …

There is the Chromatic Convergence Theorem by Hopkins and Ravanel which states that the homotopy inverse limit of the chromatic tower of a finite spectra $X$ is $X$. Let's call any spectra with this …