Variations on a Theorem of Tate (Memoirs of the American Mathematical Society)

by: Stefan Patrikis (Author)

Publisher: Amer Mathematical Society

Publication Date: 2019/4/1

Language: English

Print Length: 156 pages

ISBN-10: 1470435403

ISBN-13: 9781470435400

Book Description

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.

About the Author

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.