{"product_id":"9781470435400","title":"Variations on a Theorem of Tate","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.","brand":"Stefan Patrikis","offers":[{"title":"Default Title","offer_id":46776561467710,"sku":"9781470435400","price":0.0,"currency_code":"ZAR","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4357\/7662\/products\/9781470435400_cfaeca28-865c-4d77-8315-fbd5c9a16143.jpg?v=1707476989","url":"https:\/\/exclusivebooks.co.za\/products\/9781470435400","provider":"Exclusive Books Online","version":"1.0","type":"link"}