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Riemann-Roch for homotopy invariant K-theory and Gysin morphisms
We prove the Riemann-Roch theorem for homotopy invariant $K$-theory and projective local complete intersection morphisms between finite dimensional noetherian schemes, without smoothness assumptions.Expand
Lovelock's theorem revisited
Let (X,g) be an arbitrary pseudo-riemannian manifold. A celebrated result by Lovelock ([4], [5], [6]) gives an explicit description of all second-order natural (0,2)-tensors on X, that satisfy theExpand
Uniqueness of the Gauss–Bonnet–Chern formula (after Gilkey–Park–Sekigawa)
Abstract On an oriented Riemannian manifold, the Gauss–Bonnet–Chern formula establishes that the Pfaffian of the metric represents, in de Rham cohomology, the Euler class of the tangent bundle.Expand
Natural operations on holomorphic forms
We prove that the only natural differential operations between holomorphic forms on a complex manifold are those obtained using linear combinations, the exterior product and the exteriorExpand
On the higher Riemann-Roch without denominators.
We prove two refinements of the higher Riemann-Roch without denominators: a statement for regular closed immersions between arbitrary finite dimensional noetherian schemes, with no smoothnessExpand
Commutative monoids and their corresponding affine $$\Bbbk $$-schemes
In this expository note, we give a self-contained presentation of the equivalence between the opposite category of commutative monoids and that of commutative, monoid $$\Bbbk $$ -schemes that areExpand
Ju l 2 01 4 Dimensional curvature identities on pseudo-Riemannian geometry
For a fixed n ∈ N, the curvature tensor of a pseudo-Riemannian metric, as well as its covariant derivatives, satisfy certain identities that hold on any manifold of dimension less or equal than n. InExpand
Dimensional curvature identities on pseudo-Riemannian geometry
Abstract For a fixed n ∈ N , the curvature tensor of a pseudo-Riemannian metric, as well as its covariant derivatives, satisfies certain identities that hold on any manifold of dimension less than orExpand
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