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14 votes
0 answers
362 views

Comparing algebraic and analytic spaces through the universal property of classifying topoi

$\newcommand\kAlg{k\mathrm{Alg}}\DeclareMathOperator\Zar{Zar}\newcommand\Mnf{\mathrm{Mnf}}$I apologize beforehand if my question is naïve. I must admit that I do not know much about analytic/smooth ...
Nico's user avatar
  • 775
5 votes
0 answers
156 views

$\mathscr{D}$-module external tensor product and analytification

Let $X$ and $Y$ be smooth complex varieties and $M\in D^b_{\mathrm{hol}}(\mathscr{D}_X)$ resp. $N\in D^b_{\mathrm{hol}}(\mathscr{D}_Y)$ holonomic $\mathscr{D}$-modules (resp. complexes with holonomic ...
user178979's user avatar
6 votes
0 answers
274 views

Does the cohomology comparison part of GAGA hold over the reals?

If $k=\mathbb{C}$, $X$ is a projective (or even proper) scheme over $k$ and $F$ a coherent sheaf on $X$, then there is an isomorphism $$ H^p(X,F)\rightarrow H^p(X^{an}, F^{an}) $$ (and there is also ...
jorst's user avatar
  • 359