Higher algebraic ktheory of schemes and of derived categories r. Higher algebraic ktheory of admissible abelian categories. Pdf higher algebraic ktheory after quillen, thomason. This paper is concerned with higher algebraic ktheory and actions of algebraic groups g on such nice categories as the category of algebraic vector bundles on a scheme x. A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext. Higher algebraic ktheory after quillen, thomason and others marco schlichting mathematics institute, zeeman building, university of warwick, coventry cv4 7al uk, m.
In contrast, finding the correct definition of the higher kgroups of rings was a. Quillen ql discovered the higher atheory of exact categories in a form which did not. For quillens ktheory, quillen showed in q that applying the functor. There is a very nice generalization of the thomasontrobaugh theorem which is due. Ktheory itself, rather than on these applications of algebraic ktheory. Higher chow groups form, not a cohomology theory, but a borelmoore. Our emphasis is on the application of triangulated category methods in algebraic ktheory. Am72, volume 72 by john milnor, 9780691081014, available at book depository with free delivery worldwide. Algebraic ktheory of rings of integers in local and global fields pdf.
Algebraic ktheory is a subject area in mathematics with connections to geometry, topology. Higher algebraic ktheory of schemes and of derived categories. Quillens localisation theorem in algebraic ktheory is considerably easier to prove. Thomason and thomas trobaugh to alexander grothendieck on his 60th birthday in this paper we prove a localization theorem for the atheory of com mutative rings and of schemes, theorem 7. A universal characterization of higher algebraic ktheory. We present an introduction with a few proofs to higher algebraic ktheory of schemes based on the work of quillen, waldhausen, thomason and others. Higher algebraic ktheory of admissible abelian categories and localization theorems dongyuan yao. Khomology theory and algebraic ktheory request pdf. An introduction to algebraic ktheory christian ausoni. In this paper we prove a localization theorem for the ktheory of commutative rings and of schemes, theorem 7. Download limit exceeded you have exceeded your daily download allowance. Algebraic ktheory, algebraic cycles and arithmetic geometry.
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