Variations on a Theorem of Tate
- ISBN-10
- 1470435403
- ISBN-13
- 9781470435400
- Category
- Algebraic number theory
- Pages
- 156
- Language
- English
- Published
- 2019-04-10
- Publisher
- American Mathematical Soc.
- Author
- Stefan Patrikis
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 Gal(F¯¯¯¯/F)→PGLn(C) lift to GLn(C). 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 on: possible infinity-types of algebraic automorphic representations; comparison of the automorphic and Galois “Tannakian formalisms” monodromy (independence-of-ℓ) questions for abstract Galois representations.
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