{"product_id":"neron-models-comprehensive-survey-of-neron-models-and-construction","title":"Neron Models - Comprehensive Survey of Neron Models and Construction","description":"\u003cp\u003eIn this review of Neron Models the reviewer finds a deep, carefully argued treatment aimed at researchers and advanced students of arithmetic algebraic geometry; the single biggest reason to buy is the book's thorough construction of Neron models from Grothendieck's perspective, which makes it a valuable reference for anyone working on integral structures of abelian varieties. The tone throughout is scholarly and methodical, and the text is best appreciated by readers with a solid background in algebraic geometry who need a rigorous account rather than an introductory overview.\u003c\/p\u003e\n\n\u003ch2\u003eKey Features\u003c\/h2\u003e\n\u003cul\u003e\n \u003cli\u003e\n\u003cstrong\u003eComprehensive construction:\u003c\/strong\u003e Presents a detailed, step-by-step construction of \u003cstrong\u003eNeron models\u003c\/strong\u003e using Grothendieck's algebraic geometry framework, which clarifies foundational points for specialists.\u003c\/li\u003e\n \u003cli\u003e\n\u003cstrong\u003eHistorical context:\u003c\/strong\u003e Explains that Neron models were introduced by A. Neron in the early 1960s and situates the subject within later developments in arithmetic geometry.\u003c\/li\u003e\n \u003cli\u003e\n\u003cstrong\u003eFocus on integral structure:\u003c\/strong\u003e Emphasizes the integral aspects of abelian varieties over number fields, making it useful for researchers studying arithmetic properties.\u003c\/li\u003e\n \u003cli\u003e\n\u003cstrong\u003eAdvanced audience orientation:\u003c\/strong\u003e Written for arithmeticians and algebraic geometers, the exposition assumes familiarity with schemes and related tools, enabling concise yet rigorous arguments.\u003c\/li\u003e\n \u003cli\u003e\n\u003cstrong\u003eSecond-part connections:\u003c\/strong\u003e Develops the relationship between Neron models and the relative theories introduced earlier, helping readers apply the construction in broader contexts.\u003c\/li\u003e\n\u003c\/ul\u003e\n\n\u003ch2\u003eWho It's For\u003c\/h2\u003e\n\u003cp\u003eThis book is primarily for graduate students, postdocs, and established researchers in \u003cstrong\u003ealgebraic geometry\u003c\/strong\u003e and arithmetic geometry who need a definitive reference on Neron models and their construction. It is especially useful when one requires a precise account rooted in Grothendieck's language and for work on abelian varieties over number fields.\u003c\/p\u003e\n\u003cp\u003eThose seeking an elementary introduction or a gentle pedagogical text on abelian varieties should look elsewhere; the treatment here is not a primer and assumes substantial background in schemes, cohomology, and arithmetic geometry.\u003c\/p\u003e\n\n\u003ch2\u003ePros \u0026amp; Cons\u003c\/h2\u003e\n\u003cp\u003e\u003cstrong\u003ePros\u003c\/strong\u003e\u003c\/p\u003e\n\u003cul\u003e\n \u003cli\u003eAuthoritative, rigorous exposition that reconstructs Neron models in Grothendieck's terms.\u003c\/li\u003e\n \u003cli\u003eValuable historical and conceptual framing linking original work by A. Neron to later advances.\u003c\/li\u003e\n \u003cli\u003eUseful second-part discussion relating models to relative theories, aiding applications.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003cp\u003e\u003cstrong\u003eCons\u003c\/strong\u003e\u003c\/p\u003e\n\u003cul\u003e\n \u003cli\u003eRequires prior advanced background, so it is not accessible as an introductory text for newcomers.\u003c\/li\u003e\n\u003c\/ul\u003e\n\n\u003ch2\u003eSpecifications\u003c\/h2\u003e\n\u003ctable\u003e\n \u003ctr\u003e\n\u003ctd\u003eTitle\u003c\/td\u003e\n\u003ctd\u003eNeron Models (Ergebnisse der Mathematik und ihrer Grenzgebiete)\u003c\/td\u003e\n\u003c\/tr\u003e\n \u003ctr\u003e\n\u003ctd\u003eSeries\u003c\/td\u003e\n\u003ctd\u003eA Series of Modern Surveys in Mathematics\u003c\/td\u003e\n\u003c\/tr\u003e\n \u003ctr\u003e\n\u003ctd\u003eAuthors \/ Editors\u003c\/td\u003e\n\u003ctd\u003eSiegfried Bosch, Werner Lutkebohmert, Michel Raynaud\u003c\/td\u003e\n\u003c\/tr\u003e\n \u003ctr\u003e\n\u003ctd\u003eSubject\u003c\/td\u003e\n\u003ctd\u003eNeron models, abelian varieties, arithmetic algebraic geometry\u003c\/td\u003e\n\u003c\/tr\u003e\n \u003ctr\u003e\n\u003ctd\u003eApproach\u003c\/td\u003e\n\u003ctd\u003eConstruction via Grothendieck's algebraic geometry\u003c\/td\u003e\n\u003c\/tr\u003e\n \u003ctr\u003e\n\u003ctd\u003eIntended audience\u003c\/td\u003e\n\u003ctd\u003eArithmeticians and algebraic geometers\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/table\u003e\n\n\u003ch2\u003eOur Verdict\u003c\/h2\u003e\n\u003cp\u003eFor researchers and advanced students who need a rigorous, Grothendieck-style account of Neron models, this volume is a high-value, long-term reference that clarifies construction and relationships to relative theories; its depth and precision justify the purchase for specialists, while those seeking an elementary introduction should consider more introductory texts first.\u003c\/p\u003e\n\n\u003ch2\u003eFrequently Asked Questions\u003c\/h2\u003e\n\u003cp\u003e\u003cstrong\u003eDoes this book cover the original construction by A. Neron?\u003c\/strong\u003e\u003cbr\u003eYes, the review notes that the volume treats the Neron models introduced by A. Neron in the early 1960s and places them in historical context.\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003eIs the book suitable for beginners?\u003c\/strong\u003e\u003cbr\u003eNo, the book assumes significant background in algebraic geometry and is aimed at graduate-level readers and researchers.\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003eWhat perspective does the book use?\u003c\/strong\u003e\u003cbr\u003eThe treatment is given from Grothendieck's algebraic geometry perspective and develops connections to relative theories in a later part of the text.\u003c\/p\u003e","brand":"Siegfried Bosch, Werner Lutkebohmert, Michel Raynaud","offers":[{"title":"Default Title","offer_id":48660926398683,"sku":"3642080731","price":149.81,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0724\/1043\/1707\/files\/51PgHg_hbTL._SL1188.jpg?v=1778617823","url":"https:\/\/gearmusthave.com\/products\/neron-models-comprehensive-survey-of-neron-models-and-construction","provider":"GearMustHave","version":"1.0","type":"link"}