We study isomorphism classes of symplectic dual pairs P ← S → P , where P is an integrable Poisson manifold, S is symplectic, and the two maps are complete, surjective Poisson submersions with connected and simply-connected fibres. For fixed P , these Morita self-equivalences of P form a group Pic(P ) under a natural “tensor product” operation. Variants of this construction are also studied, fo...

For a Lie groupoid G over smooth manifold M we construct the adjoint action of étale # germs local bisections on algebroid g . With this action, form associated convolution C c ∞ ( ) / R -bialgebra , We represent in algebra transversal distributions This construction extends Cartier-Gabriel decomposition Hopf with finite support group.

Abstract We provide a new formalism of de Rham–Witt complexes in the logarithmic setting. This construction generalises result Bhatt–Lurie–Mathew and agrees with those Hyodo–Kato Matsuue for log-smooth schemes log-Cartier type. then use our to study monodromy action slopes Frobenius on log crystalline cohomology.

We present a definition of twisted motivic Chern classes for singular pairs (X,Δ) consisting space X and Q-Cartier divisor containing the singularities X. The is mixture construction previously defined by Brasselet-Schürmann-Yokura with multiplier ideals. are limits elliptic Borisov-Libgober. show that suitable choice Δ satisfy axioms stable envelopes in K-theory. Our an extension results prove...

For a smooth projective variety P of dimension n, we construct a Cartier divisor supported on the incidence locus in the product of Chow varieties Ca(P ) × Cn−a−1(P ). There is a natural definition of the corresponding line bundle on a product of Hilbert schemes, and we show this bundle descends to the Chow varieties. This answers a question posed by Barry Mazur. 2010 Mathematics Subject Classi...

For some reason it seem convenient to define the notion of an effective Cartier divisor before anything else. Note that in Morphisms of Spaces, Section 13 we discussed the correspondence between closed subspaces and quasi-coherent sheaves of ideals. Moreover, in Properties of Spaces, Section 28, we discussed properties of quasi-coherent modules, in particular “locally generated by 1 element”. T...

An important manifestation of Bacterium lepisepticum infection in the rabbit is pneumonia, which occurs spontaneously and is producible experimentally. In the course of our studies on the epidemiology of the disease, we have considered certain other phases of the infection--snuffles, otitis media, and the cartier state. Our present effort has been to classify pathologically the pneumonic lesion...

Suppose that X = SpecR is an F -finite normal variety in characteristic p > 0. In this paper we show that the big test ideal τb(R) = τ̃ (R) is equal to ∑ ∆ τ(R; ∆) where the sum is over ∆ such that KX + ∆ is Q-Cartier. This affirmatively answers a question asked by various people, including Blickle, Lazarsfeld, K. Lee and K. Smith. Furthermore, we have a version of this result in the case that R...