this is pretty good non-advice for reading non-math books: i.stack.imgur.com/gtDGk.jpg

Akhil Mathew proved that if $A\to B$ is an étale map of $E_\infty$ R-algebras, then $THH^R(A)\otimes_A B \to THH^R(B)$ is an equivalence, generalizing a theorem of McCarthy-Minasian which works for connective algebras. Has somebody generalized McCarthy-Minasian's HKR theorem, which has a similar connective hypothesis, to the non-connective scenario?

@EricPeterson congrats!! I can't wait to get my hands on a copy in print

@ReubenStern me too! but it’ll be a while; it still has to go through a further refereeing process, and then copyediting. that’s why there’s still time to take advice :p

@EricPeterson What would you say the prerequisites are for reading your book? How much knowledge of stable homotopy theory is needed?

@Twistediso it assumes a fair amount of knowledge of the basics. it’s certainly not shy about slinging spectra around, and it takes knowledge of the Steenrod operations for granted

it’s also not shy about algebraic geometry. there it at least includes all the definitions it uses, but i’m sure it can feel quite brisk

that epigraph is wonderful

:)

if you can survive a book like Switzer or like Adams’s blue book, you are more than fine

i do remember reading adams' book and seeing that and thinking "well..."

I suppose that Adams' was not too serious with that remark, but what did he mean? speculations are welcome

he was making a comment about the amount of machinery in the field

iirc

It’s taken out of context :p in context he was talking about—yeah

Meaning that topology has more machinery or less than algebraic topology?

I would think that the former has more machinery, at least these days

the thrust was like “you might think infinite loop spaces are really hard, but at least you don’t have to read whole tomes to understand the basic framework!”

Yeah, times change

And even snider youngsters take your snide remarks out of context

"The apparatus of definitions, theorems and proofs needed to carry out the programme in detail demands a capital investment of intellectual work which may seem daunting to those not directly concerned; many readers may be able to remember feeling the same way about spectral sequences, sheaf theory or whatever is now their favourite tool; let us be glad we don't work in algebraic geometry."

Funny, that's how I think of stable homotopy theory these days...

to be fair to adams algebraic geometry had just exploded in complexity over the previous 20 years or so

@PeterNelson It's really hard to beat Adams when it comes to snide-yet-accurate side remarks!