Steven L. Kleiman

A term of Commutative Algebra

Altman, Allen; Kleiman, Steven (Worldwide Center of Mathematics, 2021-04-11)

There is no shortage of books on Commutative Algebra, but the present book is different. Most books are monographs, with extensive coverage. But there is one notable exception: Atiyah and Macdonald's 1969 classic. It ...
Two formulas for the BR multiplicity

Kleiman, Steven L. (Springer-Verlag, 2016-07)

We prove a projection formula, expressing a relative Buchsbaum–Rim multiplicity in terms of corresponding ones over a module-finite algebra of pure degree, generalizing an old formula for the ordinary (Samuel) multiplicity. ...
The Picard Scheme

Kleiman, Steven L. (2013-09)

This article introduces, informally, the substance and the spirit of Grothendieck's theory of the Picard scheme, highlighting its elegant simplicity, natural generality, and ingenious originality against the larger ...