{"product_id":"pseudo-reductive-groups-hardback-9781107087231","title":"Pseudo-reductive Groups (Hardback) 9781107087231","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003ePseudo-reductive Groups\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eThis monograph provides a comprehensive treatment of the theory of pseudo-reductive groups and gives their classification in a usable form.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eBrian Conrad (Author), Ofer Gabber (Author), Gopal Prasad (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781107087231, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 4 June 2015\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e690 pages\u003cbr\u003e20.6 x 15.8 x 4.8 cm, 1.18 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e'[This book] is devoted to the elucidation of the structure and classification of pseudo-reductive groups over imperfect fields, completing the program initiated by J. Tits, A. Borel and T. Springer in the last three decades of the last century … [it] is a remarkable achievement and the definitive reference for pseudo-reductive groups. It certainly belongs in the library of anyone interested in algebraic groups and their arithmetic and geometry.' Felipe Zaldivar, MAA Reviews (maa.org\/press\/maa-reviews)\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003ePseudo-reductive groups arise naturally in the study of general smooth linear algebraic groups over non-perfect fields and have many important applications. This monograph provides a comprehensive treatment of the theory of pseudo-reductive groups and gives their classification in a usable form. In this second edition there is new material on relative root systems and Tits systems for general smooth affine groups, including the extension to quasi-reductive groups of famous simplicity results of Tits in the semisimple case. Chapter 9 has been completely rewritten to describe and classify pseudo-split absolutely pseudo-simple groups with a non-reduced root system over arbitrary fields of characteristic 2 via the useful new notion of 'minimal type' for pseudo-reductive groups. Researchers and graduate students working in related areas, such as algebraic geometry, algebraic group theory, or number theory will value this book, as it develops tools likely to be used in tackling other problems.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePreface to the second edition\u003cbr\u003e Introduction\u003cbr\u003e Terminology, conventions, and notation\u003cbr\u003e Part I. Constructions, Examples, and Structure Theory: 1. Overview of pseudo-reductivity\u003cbr\u003e 2. Root groups and root systems\u003cbr\u003e 3. Basic structure theory\u003cbr\u003e Part II. Standard Presentations and Their Applications: 4. Variation of (G', k'\/k, T', C)\u003cbr\u003e 5. Ubiquity of the standard construction\u003cbr\u003e 6. Classification results\u003cbr\u003e Part III. General Classification and Applications: 7. The exotic constructions\u003cbr\u003e 8. Preparations for classification in characteristics 2 and 3\u003cbr\u003e 9. Absolutely pseudo-simple groups in characteristic 2\u003cbr\u003e 10. General case\u003cbr\u003e 11. Applications\u003cbr\u003e Part IV. Appendices: A. Background in linear algebraic groups\u003cbr\u003e B. Tits' work on unipotent groups in nonzero characteristic\u003cbr\u003e C. Rational conjugacy in connected groups\u003cbr\u003e References\u003cbr\u003e Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Number theory [\u003ca title=\"See our other books on Number theory\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Number%20theory%20%5BPBH%5D%22\"\u003ePBH\u003c\/a\u003e], Groups \u0026amp; group theory [\u003ca title=\"See our other books on Groups \u0026amp; group theory\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Groups%20\u0026amp;%20group%20theory%20%5BPBG%5D%22\"\u003ePBG\u003c\/a\u003e], Algebra [\u003ca title=\"See our other books on Algebra\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Algebra%20%5BPBF%5D%22\"\u003ePBF\u003c\/a\u003e], Mathematics [\u003ca title=\"See our other books on Mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematics%20%5BPB%5D%22\"\u003ePB\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46265596608792,"sku":"9781107087231","price":87.59,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9781107087231i.jpg?v=1696792083","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/pseudo-reductive-groups-hardback-9781107087231","provider":"Freshly Printed Books","version":"1.0","type":"link"}