{"product_id":"splitting-and-making-explicit-the-de-rham-complex-of-the-drinfeld-space-christop-ebook","title":"Splitting and Making Explicit the de Rham Complex of the Drinfeld Space","description":"\u003cp class=\"MsoNormal\"\u003e\u003cspan style=\"font-size: 11.0pt; mso-bidi-font-family: 'Times New Roman'; color: black; mso-ligatures: standardcontextual; mso-fareast-language: EN-US;\"\u003eThis book gives a complete description of the de Rham complex of the Drinfeld space of dimension \u003cem\u003en\u003c\/em\u003e − 1 as a complex of representations of GL\u003cem\u003e\u003csub\u003en\u003c\/sub\u003e\u003c\/em\u003e(\u003cem\u003eK\u003c\/em\u003e), where \u003cem\u003en\u003c\/em\u003e ≥ 2 and \u003cem\u003eK\u003c\/em\u003e is a finite field extension of the field of \u003cem\u003ep\u003c\/em\u003e-adic numbers. The group GL\u003cem\u003e\u003csub\u003en\u003c\/sub\u003e\u003c\/em\u003e(\u003cem\u003eK\u003c\/em\u003e) acts on the Drinfeld space of dimension \u003cem\u003en\u003c\/em\u003e − 1, hence on its complex of differential forms, yielding representations of GL\u003cem\u003e\u003csub\u003en\u003c\/sub\u003e\u003c\/em\u003e(\u003cem\u003eK\u003c\/em\u003e) that mathematicians began to study in the 1980s. Understanding these representations was one of the main motivations for the development of the theory of locally analytic representations of GL\u003cem\u003e\u003csub\u003en\u003c\/sub\u003e\u003c\/em\u003e(\u003cem\u003eK\u003c\/em\u003e), which can be seen as a \u003cem\u003ep\u003c\/em\u003e-adic analogue of Harish-Chandra’s (gl\u003cem\u003e\u003csub\u003en\u003c\/sub\u003e\u003c\/em\u003e,\u003cem\u003eK\u003c\/em\u003e)-modules (in the latter, \u003cem\u003eK\u003c\/em\u003e is a maximal compact subgroup of GL\u003cem\u003e\u003csub\u003en\u003c\/sub\u003e\u003c\/em\u003e(R)). \u003c\/span\u003e\u003c\/p\u003e\n\u003cp class=\"MsoNormal\"\u003e\u003cspan style=\"font-size: 11.0pt; mso-bidi-font-family: 'Times New Roman'; color: black; mso-ligatures: standardcontextual; mso-fareast-language: EN-US;\"\u003eA transparent description is provided of the global sections of the de Rham complex of the Drinfeld space of dimension \u003cem\u003en\u003c\/em\u003e-1 as a complex of (duals of) locally analytic representations of GL\u003cem\u003e\u003csub\u003en\u003c\/sub\u003e\u003c\/em\u003e(\u003cem\u003eK\u003c\/em\u003e), and an explicit partial splitting of this complex is constructed in the derived category of (duals of) locally analytic representations of GL\u003cem\u003e\u003csub\u003en\u003c\/sub\u003e\u003c\/em\u003e(\u003cem\u003eK\u003c\/em\u003e). Multiple intermediate results on Ext groups of locally analytic representations are established, which may be useful in other contexts. Requiring a light background in locally analytic representations, modules over enveloping algebras, and rigid spaces, the book is aimed at a general audience of number theorists and representation theorists.\u003c\/span\u003e\u003c\/p\u003e","brand":"Christophe Breuil","offers":[{"title":"Default Title","offer_id":55146023584071,"sku":"9783032200952","price":80.24,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0920\/5455\/2903\/files\/splitting-and-making-explicit-the-de-rham-complex--ebook-cover.webp?v=1790226160","url":"https:\/\/www.cinebuch.de\/products\/splitting-and-making-explicit-the-de-rham-complex-of-the-drinfeld-space-christop-ebook","provider":"CineBuch","version":"1.0","type":"link"}