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Let $X$ be a geometrically integral (or geometrically reduced and geometrically connected) proper scheme over a finite field $k = \mathbb{F}_q$, so its Picard scheme exists and $\mathrm{Pic}^0_{X/k}$ …

tl;dr The Hodge-Tate comparison isomorphism relates the reduction mod $I$ of prismatic cohomology to something similar to the "Hodge-Tate cohomology" $\bigoplus_{i+j = k} H^i(X, \Omega^j_{X/K})$. Toge …

I think we can describe $P$ a bit more, using Dirichlet’s unit theorem. Since $\overline{\mathbf{Z}} = \varinjlim_{[K:\mathbf{Q}] < \infty} \mathcal{O}_K$, the same is true for the units. Now Dirichle …

These notes, from a course Fargues taught at Chicago and transcribed by Sean Howe, are very nice and make a very strong effort to motivate this conjecture and the surrounding theory by analogy with 'h …

I am currently learning some aspects of the theory of complex multiplication for elliptic curves, and the relationship with class field theory. As I understand it, there is a very special class of el …