I will talk about the problem of classifying local systems of geometric origin on algebraic varieties over complex numbers.

Conjecture: For a smooth algebraic variety S over a finitely generated field F, a semi-simple Q_l-local system on S_{\bar{F}} is of geometric origin if and only if it extends to a local system on S_{F'} for a finite extension F' \supset F.

My main goal will be to provide motivation for this conjecture arising from the Fontaine-Mazur conjecture, and survey known results and related problems.

Zoom 链接: https://us02web.zoom.us/j/82749153248?pwd=eE9ITTlCMVBCbXNIblVoaVVIS2F5dz09
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