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ag.algebraic geometry – A de Rham area for meromorphic connections? Answer

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ag.algebraic geometry – A de Rham area for meromorphic connections?

To any area $X$ you possibly can affiliate its de Rham area $X_{dR}$. Vector bundles on $X_{dR}$ are the identical factor as vector bundles on $X$ with a flat connection.

Can something love this breathe stated for meromorphic connections?


For occasion, a simple thought is that there energy actually breathe an area $X_{mdR}$ whose vector bundles are vector bundles on $X$ with a flat meromorphic connection. Then there would breathe maps $eta_{dR}to X_{mdR}to X_{dR}$, the place $eta$ is the universal level of $X$ (on which all meromorphic bundles are holomorphic), suggesting that perhaps $X_{mdR}$ might breathe constructed as some systematize of thickening of $X_{dR}$ in $eta_{dR}$.

I’m cognizant that Deligne has a construction theorem for normal meromorphic connections, so perhaps it is extra affordable to limit to the common meromorphic illustration.

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