Variations on a Theorem of Tate
Stefan Patrikis, "Variations on a Theorem of Tate "
English | ISBN: 1470435403 | 2019 | 156 pages | PDF | 2 MB
English | ISBN: 1470435403 | 2019 | 156 pages | PDF | 2 MB
Let $F$ be a number field. These notes explore Galois-theoretic, automorphic, and motivic analogues and refinements of Tate's basic result that continuous projective representations $mathrmGal(overlineF/F) to mathrmPGLn(mathbbC)$ lift to $mathrmGLn(mathbbC)$. The author takes special interest in the interaction of this result with algebraicity (for automorphic representations) and geometricity (in the sense of Fontaine-Mazur). On the motivic side, the author studies refinements and generalizations of the classical Kuga-Satake construction. Some auxiliary results touch possible infinity-types of algebraic automorphic representations; comparison of the automorphic and Galois Tannakian formalisms'' monodromy (independence-of-$ell$) questions for abstract Galois representations.