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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 $f$ …

I want to offer a possibly heretical opinion based on conversations I've had with people who do algebraic geometry, especially Joe Harris. I think that it is not necessary to know very much commutativ …

I am curious about stacky generalizations of the following GAGA theorem: If $X, U$ are complex algebraic varieties of finite type, $X$ is proper and $f:X\to U$ is an analytic map then $f$ is algeb …

This is an improved version of this question. Maybe it should be an edit -- I'm not sure what the MO convention is. I'm curious, more or less, how much information one can get out of the derived cate …

I'll go ahead and turn my comment into an answer. It does form a monad, but (probably) not a very interesting one. Namely, first note that any pair of adjoint functors $L:\mathcal{C}\leftrightarrows \ …

Say $X$ is a smooth projective variety and $\beta\in H_2(X)$ is a class. Then there is a finite-type proper scheme (or in general, stack) $SM : = \overline{\mathcal{M}}_{g,n}(X,\beta)$ of stable maps …

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 …

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 …

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 $U$ 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 …

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 …

Say we are working with schemes over a field $k\subset \mathbb{C}.$ A motive in the sense of Voevodsky is a functor $Sch\to D^bVect$ from (an appropriate category of) schemes to the DG category of com …

A stack is an object that mixes the notions of (algebraic) space and group. The key insight of stack theory is that most things you would want to do with spaces you can do with stacks: namely, you hav …

Let $M_{g, n}$ be the moduli space of curves of genus $g$ with $n$ marked points. Let $M_{g, \vec{n}}$ be the moduli space of marked curves with a choice of a (possibly zero) tangent vector at each ma …

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 …