Multiplicities and Chern classes in local algebra /
Roberts, Paul, Ph. D.,
Multiplicities and Chern classes in local algebra / Multiplicities & Chern Classes in Local Algebra Paul C. Roberts. - Cambridge : Cambridge University Press, 1998. - 1 online resource (xi, 303 pages) : digital, PDF file(s). - Cambridge tracts in mathematics ; 133 . - Cambridge tracts in mathematics ; 133. .
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Prime ideals and the Chow group -- Graded rings and Samuel multiplicity -- Complexes and derived functors -- Homological properties of rings and modules -- Intersection multiplicities -- The homological conjectures -- The Frobenius map -- Projective schemes -- Chern classes of locally free sheaves -- The Grassmannian -- Local Chern characters -- Properties of local Chern characters -- Applications and examples.
The theory of local Chern characters used in commutative algebra originated in topology some years ago, and from there was introduced in algebraic geometry. This book describes the theory in an algebraic setting, presenting research results and important algebraic applications, some of which come from the author's own work. It concentrates on the background in commutative algebra and homological algebra and describes the relations between these subjects, including extensive discussions of the homological conjectures and of the use of the Frobenius map.
9780511529986 (ebook)
Multiplicity (Mathematics)
Chern classes.
Commutative algebra.
QA251.38 / .R64 1998
512/.24
Multiplicities and Chern classes in local algebra / Multiplicities & Chern Classes in Local Algebra Paul C. Roberts. - Cambridge : Cambridge University Press, 1998. - 1 online resource (xi, 303 pages) : digital, PDF file(s). - Cambridge tracts in mathematics ; 133 . - Cambridge tracts in mathematics ; 133. .
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Prime ideals and the Chow group -- Graded rings and Samuel multiplicity -- Complexes and derived functors -- Homological properties of rings and modules -- Intersection multiplicities -- The homological conjectures -- The Frobenius map -- Projective schemes -- Chern classes of locally free sheaves -- The Grassmannian -- Local Chern characters -- Properties of local Chern characters -- Applications and examples.
The theory of local Chern characters used in commutative algebra originated in topology some years ago, and from there was introduced in algebraic geometry. This book describes the theory in an algebraic setting, presenting research results and important algebraic applications, some of which come from the author's own work. It concentrates on the background in commutative algebra and homological algebra and describes the relations between these subjects, including extensive discussions of the homological conjectures and of the use of the Frobenius map.
9780511529986 (ebook)
Multiplicity (Mathematics)
Chern classes.
Commutative algebra.
QA251.38 / .R64 1998
512/.24