# Tagged Questions

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### Definition of ind-schemes

What is the correct definition of an ind-scheme? I ask this because there are (at least) two definitions in the literature, and they really differ. Definition 1. An ind-scheme is a directed colimit ...
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### How algebraic is the holonomy map?

Let $G$ be either a compact, simple, simply-connected Lie group, or a simply-connected complex reductive group (so either $SU(n)$ or $SL(n,\mathbb{C})$, for instance), or even complex affine. I don't ...
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### infinite dimensional germs of schemes and tangent spaces

(The question of the type "how to define?") Let $(R,\mathfrak{m})$ be a local ring over a field $k$ of zero characteristic. Consider the matrices over this ring, $Mat(m,R)$. I think of $Mat(m,R)$ as ...
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### Infinite Dimensional Weil Restriction and Ind-scheme

I'm studying the Weil Restriction $\mbox{Res}_{k/\textbf{F}_p}$ where $\textbf{F}_p$ is the field with $p$ elements and $k$ is a perfect field over $\textbf{F}_p$, not necessarily finite. In this ...
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### Is there an underlying topological space for ind-schemes?

An ind-scheme over a base scheme $S$ can be defined in several ways. For simplicity, lets assume that $S$ is the spectrum of an algebraically closed field $k$. We can define a $k$-ind-scheme as a ...
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### ind scheme and Jacobson property

Let $G$ a semisimple group over $k$ and $k$ algebraically closed. Let $G(k((t)))$ the corresponding ind-scheme, does it satisfies the Jacobson property, say closed points are dense in it?
Let $X$ a ind-scheme of ind-finite type and ind-affine. (e.g, take a k- smooth, affine scheme of finte type $T$, $C$ a smooth projective curve over $k$ and $x$ a closed point, then $X=T(C-x)$ verifies ...