Abstract: 

We prove that the monodromy of a cohomologically rigid integrable connection  on a smooth complex projective variety is integral. This answers positively a special case of a conjecture by Carlos Simpson. To this aim, we use $F$-isocrystals and $\ell$-adic companions. Joint with Michael Groechenig.

Hélène Esnault is currently the Einstein Professor in Free University of Berlin. She is recognised as an international leader in arithmetic geometry. She has received many awards, including the Leibniz Prize (2003), ERC advanced grant (2009). She spoke in 2002 ICM and 2012 ECM. She is also a member of the German National Academy as well the Academy of Europe.