By B. Brent Gordon, James D. Lewis, Stefan Muller-Stach, Shuji Saito, Noriko Yui

The NATO ASI/CRM summer season institution at Banff provided a special, complete, and in-depth account of the subject, starting from introductory classes through prime specialists to discussions of the newest advancements by way of all contributors. The papers were geared up into 3 different types: cohomological equipment; Chow teams and causes; and mathematics tools. As a subfield of algebraic geometry, the speculation of algebraic cycles has passed through a variety of interactions with algebraic $K$-theory, Hodge concept, mathematics algebraic geometry, quantity concept, and topology.These interactions have resulted in advancements equivalent to an outline of Chow teams when it comes to algebraic $K$-theory; the applying of the Merkurjev-Suslin theorem to the mathematics Abel-Jacobi mapping; development at the celebrated conjectures of Hodge, and of Tate, which compute cycles category teams respectively by way of Hodge thought or because the invariants of a Galois team motion on etale cohomology; and, the conjectures of Bloch and Beilinson, which clarify the 0 or pole of the $L$-function of a spread and interpret the prime non-zero coefficient of its Taylor enlargement at a severe aspect, by way of mathematics and geometric invariant of the range and its cycle type teams. The great contemporary development within the thought of algebraic cycles relies on its many interactions with numerous different parts of arithmetic. This convention used to be the 1st to target either mathematics and geometric points of algebraic cycles. It introduced jointly top specialists to talk from their a number of issues of view. a distinct chance used to be created to discover and examine the intensity and the breadth of the topic. This quantity provides the fascinating effects.

Show description

Read Online or Download The Arithmetic and Geometry of Algebraic Cycles: Proceedings of the Crm Summer School, June 7-19, 1998, Banff, Alberta, Canada (Crm Proceedings and Lecture Notes) PDF

Best Algebraic Geometry books

Analytic K-Homology (Oxford Mathematical Monographs)

This paintings attracts jointly rules from algebraic topology, practical research and geometry. it's a software - a method of conveying info between those 3 matters - and it's been used with good fortune to find theorems throughout a large span of arithmetic. the aim of this booklet is to acquaint the reader with the fundamental principles of analytic K-homology and boost a few of its functions.

The Geometry of Syzygies: A Second Course in Algebraic Geometry and Commutative Algebra (Graduate Texts in Mathematics)

First textbook-level account of uncomplicated examples and methods during this sector. compatible for self-study via a reader who is aware a bit commutative algebra and algebraic geometry already. David Eisenbud is a widely known mathematician and present president of the yank Mathematical Society, in addition to a profitable Springer writer.


"It offers a delicate portrait of a good man or woman. It describes correctly and intelligibly on a nontechnical point the realm of mathematical rules within which Hilbert created his masterpieces. And it illuminates the heritage of German social heritage opposed to which the drama of Hilberts lifestyles used to be performed.

Introduction to Analysis of the Infinite: Book I

From the preface of the writer: ". .. i've got divided this paintings into books; within the first of those i've got restrained myself to these issues pertaining to natural research. within the moment ebook i've got defined these factor which needs to be recognized from geometry, when you consider that research is typically built in any such manner that its software to geometry is proven.

Additional info for The Arithmetic and Geometry of Algebraic Cycles: Proceedings of the Crm Summer School, June 7-19, 1998, Banff, Alberta, Canada (Crm Proceedings and Lecture Notes)

Show sample text content

Rated 4.90 of 5 – based on 17 votes