# Posts Tagged: profinite

• stories

## the Reddit (after)effect

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Sunday january 2nd around 18hr NeB-stats went crazy. Referrals clarified that the post ‘What is the knot associated to a prime?’ was picked up at Reddit/math and remained nr.1 for about a day. Now, the dust has settled, so let’s learn from the experience. A Reddit-mention is to a blog what doping is to a… Read more »

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## What is the knot associated to a prime?

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Sometimes a MathOverflow question gets deleted before I can post a reply… Yesterday (New-Year) PD1&2 were visiting, so I merely bookmarked the What is the knot associated to a prime?-topic, promising myself to reply to it this morning, only to find out that the page no longer exists. From what I recall, the OP interpreted… Read more »

• absolute, geometry, number theory

## Mazur’s knotty dictionary

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The algebraic fundamental group of a scheme gives the Mazur-Kapranov-Reznikov dictionary between primes in number fields and knots in 3-manifolds.

• absolute, geometry, noncommutative

## noncommutative F_un geometry (1)

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We propose to extend the Connes-Consani definition to noncommuntative F_un varieties.

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A quick recap of last time. We are trying to make sense of affine varieties over the elusive field with one element $\mathbb{F}_1$, which by Grothendieck’s scheme-philosophy should determine a functor $\mathbf{nano}(N)~:~\mathbf{abelian} \rightarrow \mathbf{sets} \qquad A \mapsto N(A)$ from finite Abelian groups to sets, typically giving pretty small sets $N(A)$. Using the… Read more »

• absolute, groups

## F_un and braid groups

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Recall that an n-braid consists of n strictly descending elastic strings connecting n inputs at the top (named 1,2,…,n) to n outputs at the bottom (labeled 1,2,…,n) upto isotopy (meaning that we may pull and rearrange the strings in any way possible within 3-dimensional space). We can always change the braid slightly such that we… Read more »

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## Bost-Connes for ringtheorists

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Over the last days I’ve been staring at the Bost-Connes algebra to find a ringtheoretic way into it. Ive had some chats about it with the resident graded-guru but all we came up with so far is that it seems to be an extension of Fred’s definition of a ‘crystalline’ graded algebra. Knowing that several… Read more »

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