Integrality of the Chern character in small codimension

Abstract

We prove an integrality property of the Chern character with values in Chow groups. As a consequence we obtain, for a prime number p, a construction of the p-1 first homological Steenrod operations on Chow groups modulo p and p-primary torsion, over an arbitrary field. We provide applications to the study of correspondences between algebraic varieties.Comment: Correct some typos; add an appendix extending the results to schemes of finite type over a regular bas

Degree formula for the Euler characteristic

“…When the dimension of X is < p(p − 1), where p is the characteristic of the base field, one can also use [Hau11] to obtain the same result, over any field. …”

Fixed point theorems involving numerical invariants

“…The group is generated by classes for a closed subscheme of (see [SGA6, X, Corollaire 1.1.4]). By [Hau12, Proposition 9.1], for such the integer is congruent modulo to the degree of some zero-cycle supported on , and in particular on .◻…”

Rational maps between quasilinear hypersurfaces

“…Remark 6.13. In a recent article [Hau11], O. Haution has shown that any degree p hypersurface of dimension p − 1 (over an arbitrary field) which has no closed points of degree prime to p is strongly p-incompressible. In particular, an anisotropic quasilinear p-hypersurface of dimension p − 1 is strongly p-incompressible.…”