Can I keep my Indian demat account after I move to the United States?

You can, but it must be re-designated to NRI status — you cannot keep a resident demat account once you're a non-resident. That means converting to an NRI demat linked to an NRE or NRO account, often under the Portfolio Investment Scheme for buying and selling listed shares. Holding individual Indian stocks this way avoids the PFIC problem (stocks aren't PFICs), but any Indian mutual fund units sitting in that demat are PFICs and create the punitive US tax and Form 8621 burden. You'll also disclose the demat holdings on FBAR and possibly Form 8938, and report Indian capital gains and TDS on your US return with a foreign tax credit. The key compliance step is the resident-to-NRI conversion; continuing to trade on a resident demat after moving creates regulatory problems on the Indian side.