In algebraic geometry, Kleiman's theorem, introduced by Kleiman (1974), concerns dimension and smoothness of scheme-theoretic intersection after some perturbation...

various ways. For example, a result due to Steven Kleiman asserts the following (cf. Kleiman's theorem): for a connected algebraic group G, and any homogeneous...

replacing a divisor by a suitable linearly equivalent divisor (cf. Kleiman's theorem.) Serre's inequality above may fail in general for a non-regular ambient...

The Riemann–Roch theorem is an important theorem in mathematics, specifically in complex analysis and algebraic geometry, for the computation of the dimension...

R.) Kleiman's criterion fails for proper algebraic spaces X over a field, even if X is smooth. On a projective scheme X over a field, Kleiman's criterion...

{\displaystyle f} is of relative dimension n {\displaystyle n} . Kleiman's theorem Glossary of scheme theory Equidimensional ring The Spec of the symmetric...

doi:10.1007/s002220050335, S2CID 7215999. Cone of curves (Kleiman-Mori cone) Kleiman's theorem Duren, Peter L.; Askey, Richard (1989), A Century of Mathematics...

In mathematics, the cone of curves (sometimes the Kleiman-Mori cone) of an algebraic variety X {\displaystyle X} is a combinatorial invariant of importance...

In category theory, a branch of mathematics, Beck's monadicity theorem gives a criterion that characterises monadic functors, introduced by Jonathan Mock...

the theorem of the cube was first published by Lang (1959), who credited it to André Weil. A discussion of the history has been given by Kleiman (2005)...

different ways a variety can be embedded into projective space. One answer is Kleiman's criterion (1966): for a projective scheme X over a field, a line bundle...

cohomology with constant coefficients Kleiman 2005, Definition 9.2.2. Grothendieck, A. (1962), V. Les schémas de Picard. Théorèmes d'existence, Séminaire Bourbaki...

\Omega _{X/k}} . The Riemann–Roch theorem and its far-reaching generalization, the Grothendieck–Riemann–Roch theorem, contain as a crucial ingredient the...

if it is both a Noetherian module and an Artinian module (cf. Hopkins' theorem). Since all Artinian rings are Noetherian, this implies that a ring has...

Hartshorne (1977), Proposition II.6.2. Stacks Project, Tag 02RS. Kleiman (2005), Theorems 2.5 and 5.4, Remark 6.19. Hartshorne (1977), Example II.6.5.2....

elementary to the more advanced, include: Dimension counting Bézout's theorem Schubert calculus, and more generally characteristic classes in cohomology...

numbers. One of the axioms of a Weil theory is the so-called hard Lefschetz theorem (or axiom): Begin with a fixed smooth hyperplane section W = H ∩ X, where...

definition of intersection number in order to state results like Bézout's theorem. The intersection number is obvious in certain cases, such as the intersection...

on descent theory, and existence theorems including that for the Hilbert scheme. The Technique de descente et théorèmes d'existence en géometrie algébrique...

computations in this case, for example in Altman & Kleiman (1970, Ch. VIII, p. 177). Tate (1968) proves the theorem using a notion of traces for certain endomorphisms...

Springer-Verlag. ISBN 978-0-387-97495-8. MR 1153249. Fulton–Hansen connectedness theorem Announcement of the 1996 Steele Prizes at the American Mathematical Society...

on algebraic cycles (Kleiman 1968). However, Grothendieck's standard conjectures remain open (except for the hard Lefschetz theorem, which was proved by...

dimension over R is finite) are the real numbers and the quaternions by a theorem of Frobenius, while any matrix ring over the reals or quaternions – M(n...

Bertini at the Mathematics Genealogy Project Bertini and his two fundamental theorems by Steven L. Kleiman, on the life and works of Eugenio Bertini...

with any algebraic numerical coefficients 12. Extensions of Kronecker's theorem on Abelian fields to any algebraic realm of rationality 13. Impossibility...

cohomology of schemes" (PDF), in Giraud, Jean; Grothendieck, Alexander; Kleiman, Steven L.; et al. (eds.), Dix Exposés sur la Cohomologie des Schémas,...

varieties play an outstanding role in the Langlands program. The prototypical theorem, the Eichler–Shimura congruence relation, implies that the Hasse–Weil zeta...

900, 1982 (therein by Deligne: Tannakian Categories) Arithmetic Duality Theorems, Academic Press, Perspectives in Mathematics, 1986 Editor with Laurent...

choice of very ample line bundle L {\displaystyle {\mathcal {L}}} . It is a theorem of Grothendieck's that the functors Q u o t E / X / S Φ , L {\displaystyle...

ISBN 978-2-85629-164-1, MR 2115000 Voevodsky, V. (1995), "A nilpotence theorem for cycles algebraically equivalent to 0", Int. Math. Res. Notices, 4:...