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More at field with one element, after creating person entry Christophe Soulé about the creator. By the way the Soulé has different encoding in n-Forum than in nlab so the link does not access the right page from here. See redirect Christophe Soule.
New related entry Riemann hypothesis. I plan to have Riemann zeta function separetely from zeta function as the latter may refer to much wider range of zeta functions of dynamical systems, L-functions of varieties, various arithmetic zeta functions, zeta functions in the operator theory and so on…all of which have some related ideas.
Created number theory. I crudely allude to Matijasevich’s theorem; foundational experts whose presence in $n$lab is widely felt are invited to improve it.
Added some possibly controversial remarks to discrete mathematics refering to number theory.
More references (including a short video of Connes) at field with one element.
I added redirects absolute algebraic geometry and absolute geometry. Though it is in principle different to talk about geometry over $\mathbf{F}_1$ and on $\mathbf{F}_1$, in practice it is always convoluted so it is better not to artifically split. New entry blueprint with redirect blue scheme.
I have edited the very first sentence at field with one element in an attempt to make it be clearer: now it reads:
Jacques Tits first observed that many identities coming from algebraic geometry (and particularly algebraic groups) over finite fields $\mathbb{F}_q$ made perfect sense as expressions in $q$ when extrapolated to the case $q=1$, even though, of course, there is no actual field with a single element.
Something essential disappeared in your version:
and even correspond though, to interesting combinatorial results
If I understood right, it is not merely that one can DEFINE the extensions to $q=1$, but the values for $q=1$ were in correlation with various interesting combinatorial (i.e. counting) (and representation theoretical) facts in special cases. Though I do not know much about original Tits’ work.
More references at blueprint.
Sure, right. Sorry if I deleted that. As soon as the $n$Lab responds again (it is being very unresponsive these days…) I’ll clarify.
Also, I would prefer if the entry does not start with the words “Jacques Tits first…”. I think we should first give the facts, and then the history. Nothing against Jacques Tits, we can honor him greatly a few paragraphs below, but I think it is better style not to mix explanation of a subject with origin of a subject.
Okay, I have tried to polish the first two paragraphs a bit more. Please check if you can live with it.
I agree with you in general. But as long as we did not put the contemporary insight into contemporary motivation it was in a sense better as Tits in the first sentence. Namely as you put it now, it looks like the combinatorial identities of Tits are THE motivation for the subject, not only that there were in the beginnings. So this motivation in the first paragraph is related to an early historical phase. Now Riemann conjecture, tropical geometry, lambda rings etc. tell much more different motivation and related phenomena of stronger geometric nature, than the series in earlier works. I might be wrong. I am not suggesting that you reverse back to Tits in the first sentence but that you are aware that this is temporary state (I should think more in order to improve) and that it does mislead a bit. From next week I am at IHES for 4 weeks and hopefully I will be able to work more in nLab, though I have some urgent papers to finish and some other things as well.
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