The impact and influence of J.-P. Serres work have been notable
ever since his doctoral thesis on homotopy groups. The abundance of
findings and deep insights found in his research and survey papers
ranging from topology, several complex variables, and algebraic
geometry to number theory, group theory, commutative algebra and
modular forms, continues to provide inspiring reading for
mathematicians working in these areas, in their research and their
teaching.
Characteristic of Serres publications are the many open
questions he formulates pointing to further directions for
research. In four volumes of Collected Papers he has provided
comments on and corrections to most articles, and described the
current status of the open questions with reference to later
findings.
In this softcover edition of volume IV, two recently published
articles have been added, one on the life and works of Andre Weil,
the other one on Finite Subgroups of Lie Groups.
"From the reviews: "
"This is the fourth volume of J-P. Serre's "Collected Papers"
covering the period 1985-1998. Items, numbered 133-173, contain
"the essence'' of his work from that period and are devoted to
number theory, algebraic geometry, and group theory. Half of them
are articles and another half are summaries of his courses in those
years and letters. Most courses have never been previously
published, nor proofs of the announced results. The letters
reproduced, however (in particular to K. Ribet and M.-F. Vigneras),
provide indications of some of those proofs. Also included is an
interview with J-P. Serre from 1986, revealing his views on
mathematics (with the stress upon its integrity) and his own
mathematical activity. The volume ends with Notes which complete
the text by reporting recent progress and occasionally correct
it.
"Zentralblatt MATH"
"
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