Variations on a Theorem of Tate, Paperback / softback Book

Variations on a Theorem of Tate Paperback / softback

Part of the Memoirs of the American Mathematical Society series

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 $\mathrm{Gal}(\overline{F}/F) \to \mathrm{PGL}_n(\mathbb{C})$ 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.

Information

  • Format: Paperback / softback
  • Pages: 156 pages
  • Publisher: American Mathematical Society
  • Publication Date:
  • Category: Algebra
  • ISBN: 9781470435400

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