Prof. Manfred Kolster
(McMaster University)
Prof. M. Kolster will visit
McGill and Concordia Universities[‡]
during April 2000,
and give a mini-course on “K-theory
and arithmetic”. K-theory has become an
essential part of number theory,
algebra, arithmetic algebraic geometry and topology.
It generalizes some of the
most fundamental concepts in arithmetic and geometry,
e.g. class groups, unit
groups and regulators.
The mini-course will survey the theory and some of its
applications, and is
specifically designed for
the “non-specialist”. No previous knowledge of
K-theory is assumed, so that in particular students
are encouraged to attend.
The applications will focus
on the K-theory of fields, on K-groups of algebraic
integers and their relation
to special values of zeta-functions and on K-theoretic
interpretations of some
classical conjectures in number theory.
Program:
Thursday, April
13:
Special values of
zeta-functions.
Abstract: In the early 70’s
Lichtenbaum conjectured a deep relationship between
special values of
zeta-functions of number fields at negative integers and algebraic
K-theory groups, which would
generalize the classical analytic class number formula
of Dirichlet. In the talk we
describe the Conjecture and its current status.
Time & Place: Concordia University,
Library building, Room LB-540, 14:15 – 15:45 [§].
Monday, April 17:
K-theory of rings of integers in
number fields.
Abstract: This is a brief introduction to Algebraic K-theory
with special emphasis
on the K-theory of fields and of rings of
integers in number fields.
Time & Place: McGill University, Burnside Hall, Room 920,
10:00 – 11:00.
Tuesday, April
18:
Chern characters.
Abstract: One way of studying
algebraic K-theory groups is via Chern characters
into various cohomology
theories. In particular, we will discuss the étale Chern characters
of Soulé, as well as the
relation between K-theory and motivic cohomology.
Iwasawa-theory
Abstract: We briefly discuss Iwasawa
theory, in particular the so-called Main Conjecture,
and the relation to étale
cohomology.
Time & Place: McGill University, Burnside Hall, Room 920,
10:00 – 11:00 and 11:30 – 12:30.
Wednesday, April 19:[**]
The Lichtenbaum Conjecture.
Abstract: We discuss regulators and the ideas behind the
proof of the Lichtenbaum
Conjectures for abelian number fields up to
2-torsion.
The K-theory of Z and some
classical conjectures in number theory.
Abstract: We give applications
towards the structure of the K-theory groups of Z and
relations with Vandiver’s Conjecture and Leopoldt’s
Conjecture.
Time & Place: McGill University, Burnside Hall, Room 920, 10:00 – 11:00 and 11:30 – 12:30.
Eyal
Goren.