{"product_id":"algebraic-geometry-ii-cohomology-of-schemes-with-examples-and-exercises-paperback","title":"Algebraic Geometry II: Cohomology of Schemes: With Examples and Exercises - Paperback","description":"\u003cp\u003eby \u003cb\u003eUlrich Gtz\u003c\/b\u003e (Author), \u003cb\u003eTorsten Wedhorn\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003eThis book completes the comprehensive introduction to modern algebraic geometry which was started with the introductory volume \u003ci\u003eAlgebraic Geometry \u003c\/i\u003e\u003ci\u003eI: Schemes\u003c\/i\u003e.\u003cbr\u003eIt begins by discussing in detail the notions of smooth, unramified and 騁ale morphisms including the 騁ale fundamental group. The main part is dedicated to the cohomology of quasi-coherent sheaves. The treatment is based on the formalism of derived categories which allows an efficient and conceptual treatment of the theory, which is of crucial importance in all areas of algebraic geometry. After the foundations are set up, several more advanced topics are studied, such as numerical intersection theory, an abstract version of the Theorem of Grothendieck-Riemann-Roch, the Theorem on Formal Functions, Grothendieck's algebraization results and a very general version of Grothendieck duality. The book concludes with chapters on curves and on abelian schemes, which serve to develop the basics of the theory of these two important classes of schemes on an advanced level, and at the same time to illustrate the power of the techniques introduced previously.\u003cbr\u003eThe text contains many exercises that allow the reader to check their comprehension of the text, present further examples or give an outlook on further results.\u003c\/p\u003e\u003ch3\u003eBack Jacket\u003c\/h3\u003e\u003cp\u003eThis book completes the comprehensive introduction to modern algebraic geometry which was started with the introductory volume \u003ci\u003eAlgebraic Geometry \u003c\/i\u003e\u003ci\u003eI: Schemes\u003c\/i\u003e. \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003eIt begins by discussing in detail the notions of smooth, unramified and 騁ale morphisms including the 騁ale fundamental group. The main part is dedicated to the cohomology of quasi-coherent sheaves. The treatment is based on the formalism of derived categories which allows an efficient and conceptual treatment of the theory, which is of crucial importance in all areas of algebraic geometry. After the foundations are set up, several more advanced topics are studied, such as numerical intersection theory, an abstract version of the Theorem of Grothendieck-Riemann-Roch, the Theorem on Formal Functions, Grothendieck's algebraization results and a very general version of Grothendieck duality. The book concludes with chapters on curves and on abelian schemes, which serve to develop the basics of the theory of these two important classes of schemes on an advanced level, and at the same time to illustrate the power of the techniques introduced previously.\u003cbr\u003eThe text contains many exercises that allow the reader to check their comprehension of the text, present further examples or give an outlook on further results.\u003cbr\u003e\u003cb\u003eContents\u003c\/b\u003e\u003cb\u003e\u003cbr\u003e\u003c\/b\u003eDifferentials - ﾉtale and smooth morphisms - Local complete intersections - The 騁ale topology - Cohomology of sheaves of modules - Cohomology of quasi-coherent sheaves - Cohomology of projective and proper schemes - Theorem on formal functions - Duality - Curves - Abelian schemes - Appendix: Homological Algebra - Appendix: Commutative Algebra\u003cbr\u003e\u003cb\u003eAbout the Authors\u003c\/b\u003e\u003cb\u003e\u003cbr\u003e\u003c\/b\u003eProf. Dr. Ulrich Gtz, Department of Mathematics, University of Duisburg-Essen\u003cbr\u003eProf. Dr. Torsten Wedhorn, Department of Mathematics, Technical University of Darmstadt\u003ch3\u003eAuthor Biography\u003c\/h3\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eProf. Dr. Ulrich Gtz, Department of Mathematics, University of Duisburg-Essen\u003c\/p\u003e\u003cp\u003eProf. Dr. Torsten Wedhorn, Department of Mathematics, Technical University of Darmstadt\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 869\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 1.74 x 9.61 x 6.69 IN\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003eIllustrated:\u003c\/strong\u003e Yes\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e November 23, 2023\u003c\/div\u003e","brand":"Books by splitShops","offers":[{"title":"Default Title","offer_id":51777049887008,"sku":"9783658430306","price":161.98,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0974\/9764\/5344\/files\/c087dd08d1879e87d4a34f17e4b30760.webp?v=1780491214","url":"https:\/\/ebocreations.com\/products\/algebraic-geometry-ii-cohomology-of-schemes-with-examples-and-exercises-paperback","provider":"The E-Book Oasis LLC","version":"1.0","type":"link"}