# 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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