On the rationality of algebraic monodromy groups of compatible systems
Chun Yin Hui
The University of Hong Kong, Hong Kong, P.R. China
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Abstract
Let be a number field and a smooth geometrically connected variety defined over a characteristic finite field. Given an -dimensional pure -compatible system of semisimple -adic representations of the étale fundamental group of with connected algebraic monodromy groups , we construct a common -form of all the groups and in the absolutely irreducible case, a common -form of all the tautological representations . Analogous rationality results in characteristic assuming the existence of crystalline companions in for all and in characteristic zero assuming ordinariness are also obtained. Applications include the construction of a -compatible system from some -compatible system and some results predicted by the Mumford–Tate conjecture.
Cite this article
Chun Yin Hui, On the rationality of algebraic monodromy groups of compatible systems. J. Eur. Math. Soc. (2024), published online first
DOI 10.4171/JEMS/1438