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Suppose $X$ is a smooth algebraic variety (say, in characteristic $0$). It's a folklore result that $D^b\text{Coh}(X)$ is equivalent to the derived category of complexes of sheaves of $\mathcal{O}_X$- …

This is a terminology question about a class of log varieties. Given an fs (fine and saturated) log variety $(X, M)$ (for $M$ the defining sheaf of monoids), any geometric point $x\in X$ has a finitel …

There is a Serre dualizing complex $S_X\in D^b Coh(X)$ for any scheme $X$ of finite type. For proper schemes, it is characterized as the sheaf defining the right adjoint to derived global sections, an …

Suppose $U$ is a (possibly singular) scheme and $X$ is a compactification (potentially unnecessary at least in characteristic $0$). Let $\pi:X\to *$ be the map to the point (though one can consider mo …

This is a mild reformulation of a previous question. Let $R = C^\infty(\mathbb{R}^N)$ and let $I$ be an ideal in $R$ which cuts out an $n$-dimensional "singular $C^\infty$ manifold $X$" in $\mathbb{R} …

Edit The original diagonalization argument function I gave didn't satisfy the inequality. The following answer works. A diagonalization argument works here to show there aren't! Take an enumeration $X …

I'd like to characterize rational $k$-forms on a singular scheme $X$ which can be integrated on any (real) bounded submanifold that is locally LCI in $X$ in a real sense (i.e., which is the real preim …

Suppose $R$ is a perfectoid ring in mixed characteristic, and $R'$ its characteristic-$p$ tilt. Scholze's results on tilting say that the étale theories over $R$ and $R'$ are equivalent in an almost s …

Suppose $X$ is a complex projective variety with a model $X_\mathbb{Q}$ defined over the rational numbers. Then there is a rational de Rham lattice $H^k_{dR}(X_\mathbb{Q}, \mathbb{Q})\subset H^k(X, \m …

Let $k$ be an algebraically closed field of characteristic zero. Formalizing a classical folk concept, Pridham and (in a different way,) Lurie defined a formal moduli problem (over $k$) to be a functo …

I would guess that the intuition is that separable extensions extend uniquely over "infinitesimal thickenings", i.e. deformations over a nilpotent base. This makes their classification problem "rigid" …

I have a series of vague questions, related to localization of symmetric monoidal categories. Here is the context. Say we are working over a field of characteristic zero. Then the "one category leve …

Let $\tilde{X}_k$ be the normalization of the closed $k$-codimension stratum, so $\tilde{X}_0$ is the normalization of $X$. Then there is a diagram of pullback functors between the categories $\text{P …

I see this is one of your first question on MO -- welcome! The topic of the question is certainly interesting but I think you need to put a little more effort in future questions into being clear (fir …

To add a representation theory perspective: if $G$ is a Lie group, and $f$ is a function (or more precisely a distribution) on $G$ then (under certain mild conditions on $f$ and $G$), the function $f$ …