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Are we «allowed» to think of an embedding $\mathbb{Q}_p$ into $\mathbb{C}$ as something geometric like in the picture (Picture description: The $5$-adic integers $\mathbb{Z}_5$ are the pentagon dots …

Is there an analogy between the chromatic layers the sphere spectrum $\mathbb{S}$ and the ramification groups of the absolute Galois group $G(\mathbb{Q}^{\mathrm{sep}}/\mathbb{Q})$?

The Riemann zeta function can be recovered from algebraic K-theory and the Borel regulator. Analytic continuation is therefore a reasonable proceedure to do to Algebraic K-theory. How can we understan …

Is there a ring structure on $S^1=\mathbb{R}/\mathbb{Z}$?

The real J-homomorphism produces cyclic subgroups of size the denominator of $\zeta(1-2k)=-B_{2k}/k$ for $k>0$ in $\pi_{4k-1}S$ which completely account for first layer of the chromatic filtration on …

It is well known [Clausen, p-adic J-homom., in introduction] that there are cyclic subgroups of $\pi_{4k-1}S \: (k>o)$ with size the zeta values $B_{2k}/k \: (=-\zeta(1-2k))$ which completely account …

Quadratic forms play a huge role in math. This leads one to wonder: Is there a theory of cubic forms, quartic forms, quintic forms and so on? I have failed to discover any. Is there any such theory? I …

The reductive groups play a central role in the Langlands correspondence. Why are these groups called reductive? Does this name suggest something conceptual about these groups?

Frobenius modules appear in the Riemann Hilbert correspondence. Frobenius algebras appear in TQFT. Is there a way to pass from one to the other?