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2
votes
0answers
106 views

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 ...
3
votes
1answer
128 views

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 ...
5
votes
1answer
466 views

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 ...
1
vote
0answers
78 views

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?
1
vote
0answers
69 views

closed subscheme of ind scheme

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 ...
1
vote
1answer
182 views

quotient of ind scheme

Is I consider an ind scheme such as $G(k((t)))$ for a reductive connected group over $k=\bar{k}$ I have the conjugacy action of $G(k[[t]])$. In what category can I make the quotient ...
8
votes
0answers
360 views

Do smooth ind schemes have Dualizing sheafs?

Say I have an ind scheme $X = \cup_i X_i$ over a field $k$. I have its tangent bundle $\hom_k(k[\epsilon], X)$ which I can think of as ind scheme via $\cup_i \hom_k(k[\epsilon],X_i)$. The problem is ...
3
votes
1answer
314 views

Line bundles on Ind Schemes

I've learned when you have a integral smooth scheme line bundles are the same as Cartier divisors are the same as Weil divisors. My question is to what extent does this continue to hold (if at all) ...
3
votes
1answer
357 views

categorical formulation for projective ind-scheme

It is well known that Serre [FAC] gave us a nice categorical description for quasi coherent sheaves on projective scheme, it is a proj-category.(graded modules category localized by Serre subcategory) ...
3
votes
1answer
322 views

Principal bundle for contractible group is weak homotopy equivalence for ind schemes

This is may be obvious, but I am not comfortable with ind-schemes. I have an ind-scheme $X$ over $\mathbb{C}$. Every point has a neighborhood which can be written as an ascending union of regular ...