Variations on a Theorem of Tate

Stefan Patrikis (Autor)

Buch | Softcover

156 Seiten

2019
American Mathematical Society (Verlag)
978-1-4704-3540-0 (ISBN)

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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 $/mathrm{Gal}(/overline{F}/F) /to /mathrm{PGL}_n(/mathbb{C})$ lift to $/mathrm{GL}_n(/mathbb{C})$. 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-$/ell$) questions for abstract Galois representations.

Stefan Patrikis, Princeton University, NJ.

Introduction
Foundations & examples
Galois and automorphic lifting
Motivic lifting
Bibliography
Index of symbols
Index of terms and concepts.

Erscheinungsdatum	02.03.2019
Reihe/Serie	Memoirs of the American Mathematical Society
Verlagsort	Providence
Sprache	englisch
Maße	178 x 254 mm
Gewicht	248 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	1-4704-3540-3 / 1470435403
ISBN-13	978-1-4704-3540-0 / 9781470435400
Zustand	Neuware