{"product_id":"9783032200945","title":"Splitting and Making Explicit the de Rham Complex of the Drinfeld Space","description":"\u003ch3\u003eLecture Notes in Mathematics\u003c\/h3\u003e\u003ch1\u003eSplitting and Making Explicit the de Rham Complex of the Drinfeld Space\u003c\/h1\u003e\u003ch3\u003eChristophe Breuil | Zicheng Qian\u003c\/h3\u003e\u003cdiv\u003e\u003cb\u003eMathematics \/ Number Theory\u003c\/b\u003e\u003c\/div\u003e\u003cbr\u003e\u003cdiv\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;\"\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\r\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\n\u003c\/div\u003e\u003cdiv\u003e\n\u003cp\u003e\u003cstrong\u003eChristophe Breuil\u003c\/strong\u003e is the directeur de recherche CNRS at Université Paris-Saclay. His research interests include p-adic number theory, representation theory and algebraic geometry, with a focus on applications to the locally analytic, p-adic and mod p Langlands programs. He has published around 50 articles and preprints on this topic, including 4 books.\u003c\/p\u003e\r\n\u003cp\u003e\u003cstrong\u003eZicheng Qian\u003c\/strong\u003e is an assistant professor (tenure track) at the Morningside Center of Mathematics of Beijing. His research interests includemod p and p-adic aspects of the Langlands program. He has published 6 articles and preprints on this topic, including 3 books.\u003c\/p\u003e\n\u003c\/div\u003e\u003cbr\u003e\u003ctable\u003e\n\u003ctr\u003e\n\u003ctd\u003ePublication Date: \u003c\/td\u003e\n\u003ctd\u003e05 August 2026\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003ePublisher: \u003c\/td\u003e\n\u003ctd\u003eSpringer Nature Switzerland\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eImprint: \u003c\/td\u003e\n\u003ctd\u003eSpringer\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eISBN-13: \u003c\/td\u003e\n\u003ctd\u003e9783032200945\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eFormat: \u003c\/td\u003e\n\u003ctd\u003ePaperback \/ softback\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003ePage Count: \u003c\/td\u003e\n\u003ctd\u003e249\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/table\u003e","brand":"Springer Nature Switzerland","offers":[{"title":"Default Title","offer_id":46183754006668,"sku":"9783032200945","price":76.49,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783032200945.jpg?v=1781056151","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9783032200945","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}