It's the Schengen Information System - a vast EU database used by police forces in 30 countries across the border-free travel zone + (for now) the UK.
In '15 Theresa May brought the UK into SIS-II (another unlovely acronym).
That was seen as special deal for a non-Schengen country. UK police are now the third biggest users (by search function). They can ask other forces to carry out checks on criminal suspects and vice versa
And now we know things are not going well. UK is looking for exact same benefits: it wants a system with “capabilities similar to those delivered by SIS II” i.e. a real-time information exchange involving millions of bits of data. Easier said than done.
The EU says it's legally impossible to grant access to the database. Negotiators say their hands are tied by case law from the European court of justice.

If you are a non EU, non Schengen country without free movement... the answer is Non.
UK access to SIS-II also looks politically impossible. EU member states say they cannot accept any criminal justice data sharing, without the oversight of the European Court of Justice and guarantees on the European Court of Human Rights.
British sources sounded incredulous at mention of the ECJ and ECHR in relation to SIS-II.
I’m surprised they’re surprised. It is not exactly a secret that Michel Barnier has said these should underpin co-operation on criminal justice. Eg, here. https://ec.europa.eu/commission/presscorner/detail/en/SPEECH_20_340
Why is the EU hung up on ECJ and ECHR?

Because sharing data is intrusive. Allowing another police force access to information about your citizens, means politicians - and civil liberties group - want agreed process for oversight + potential breaches.
The UK would walk away from EU offer of a lesser way of info sharing, if it can’t get a SIS-II equivalent, according to EU sources.

The UK neither confirms nor denies, but says EU offer of “limited operational value”.
Both sides agree EU offer isn't as good as SIS II database or equivalent, but for the EU it's something, whereas for the UK it’s nothing.
If the UK is out of data-sharing the EU loses out too. In 2018 the UK responded to 7,000 alerts put on the SIS II system by other countries, according to UK gov stats.

But for the EU this doesn’t trump the legal and political hurdles. The ECJ case law is a red line.
If Brexit means anything... it means unstitching many, many parts of UK law and policy, then negotiating for months, years in the hope of finding a decent equivalent. But once again, the exact same benefits are proving elusive.
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