{"title":"Antoine Chambert-Loir","description":null,"products":[{"product_id":"motivic-integration-book-antoine-chambert-loir-9781493993154","title":"Motivic Integration","description":"This monograph focuses on the geometric theory of motivic integration, which takes its values in the Grothendieck ring of varieties. This theory is rooted in a groundbreaking idea of Kontsevich and was further developed by Denef \u0026amp; Loeser and Sebag. It is presented in the context of formal schemes over a discrete valuation ring, without any restriction on the residue characteristic. The text first discusses the main features of the Grothendieck ring of varieties, arc schemes, and Greenberg schemes. It then moves on to motivic integration and its applications to birational geometry and non-Archimedean geometry. Also included in the work is a prologue on p-adic analytic manifolds, which served as a model for motivic integration.  With its extensive discussion of preliminaries and applications, this book is an ideal resource for graduate students of algebraic geometry and researchers of motivic integration. It will also serve as a motivation for more recent and sophisticated theories that have been developed since.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ GARDNERS","offer_id":49735249264913,"sku":"NGR9781493993154","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52342600663313,"sku":"NLS9781493993154","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/1493993151.jpg?v=1750893028"},{"product_id":"mostly-commutative-algebra-book-antoine-chambert-loir-9783030615949","title":"(Mostly) Commutative Algebra","description":"This book stems from lectures on commutative algebra for 4th-year university students at two French universities (Paris and Rennes). At that level, students have already followed a basic course in linear algebra and are essentially fluent with the language of vector spaces over fields. The topics introduced include arithmetic of rings, modules, especially principal ideal rings and the classification of modules over such rings, Galois theory, as well as an introduction to more advanced topics such as homological algebra, tensor products, and algebraic concepts involved in algebraic geometry.   More than 300 exercises will allow the reader to deepen his understanding of the subject.      The book also includes 11 historical vignettes about mathematicians who contributed to commutative algebra.","brand":"WoB","offers":[{"title":"US \/ NEW \/ INGRAM","offer_id":51061340995857,"sku":"NIN9783030615949","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":51430416646417,"sku":"GOR014273010","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52478326374673,"sku":"NLS9783030615949","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ GOOD \/ SBYB","offer_id":52884358398225,"sku":"CIN3030615944G","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3030615944.jpg?v=1751349586"},{"product_id":"field-guide-to-algebra-book-antoine-chambert-loir-9781441919472","title":"A Field Guide to Algebra","description":"This is a small book on algebra where the stress is laid on the structure of ?elds, hence its title. Youwillhearaboutequations,bothpolynomialanddi?erential,andabout the algebraic structure of their solutions. For example, it has been known for centuries how to explicitely solve polynomial equations of degree 2 (Baby- nians, many centuries ago), 3 (Scipione del Ferro, Tartaglia, Cardan, around th 1500a.d.), and even 4 (Cardan, Ferrari,xvi century), using only algebraic operations and radicals (nth roots). However, the case of degree 5 remained unsolved until Abel showed in 1826 that a general equation of degree 5 cannot be solved that way. Soon after that, Galois de?ned the group of a polynomial equation as the group of permutations of its roots (say, complex roots) that preserve all algebraicidentitieswithrationalcoe?cientssatis?edbytheseroots.Examples of such identities are given by the elementary symmetric polynomials, for it is well known that the coe?cients of a polynomial are (up to sign) elementary symmetric polynomials in the roots. In general, all relations are obtained by combining these, but sometimes there are new ones and the group of the equation is smaller than the whole permutation group. Galois understood how this symmetry group can be used to characterize the solvability of the equation. He de?ned the notion of solvable group and showed that if the group of the equation is solvable, then one can express its roots with radicals, and conversely.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52455393132817,"sku":"NLS9781441919472","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":52749349388561,"sku":"NIN9781441919472","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781441919472.jpg?v=1759374146"},{"product_id":"motivic-integration-book-antoine-chambert-loir-9781493978854","title":"Motivic Integration","description":"This monograph focuses on the geometric theory of motivic integration, which takes its values in the Grothendieck ring of varieties.  With its extensive discussion of preliminaries and applications, this book is an ideal resource for graduate students of algebraic geometry and researchers of motivic integration.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52650802053393,"sku":"NLS9781493978854","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":53036579520785,"sku":"NIN9781493978854","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781493978854.jpg?v=1762128874"}],"url":"https:\/\/www.worldofbooks.com\/en-au\/collections\/author-books-by-antoine-chambert-loir.oembed","provider":"World of Books ","version":"1.0","type":"link"}