Titlebook: Geometric Methods in Algebra and Number Theory; Fedor Bogomolov,Yuri Tschinkel Textbook 2005 Birkhäuser Boston 2005 Area.Cohomology.Volume

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Individualistic Approaches to SuicideWe propose a conjecture combining the Mordell-Lang conjecture with an important special case of the André-Oort conjecture, and explain how existing results imply evidence for it.

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https://doi.org/10.1007/978-981-10-1825-1We propose a motivic analog of limit mixed Hodge structures. Working in the context of triangulated categories of motivic objects on schemes we introduce and study a limit motive functor and a motivic vanishing cycle sheaf.

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Material Safety Specifications,Let . be a classical Lie group and . a maximal parabolic subgroup. We describe a quantum Pieri rule which holds in the small quantum cohomology ring of .. We also give a presentation of this ring in terms of special Schubert class generators and relations. This is a survey paper which reports on joint work with Anders S. Buch and Andrew Kresch.

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,Ax-Kochen-Eršov Theorems for ,-adic integrals and motivic integration,We express the Lefschetz number of iterates of the monodromy of a function on a smooth complex algebraic variety in terms of the Euler characteristic of a space of truncated arcs.

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Nested sets and Jeffrey-Kirwan residues,For the complement of a hyperplane arrangement we construct a dual homology basis to the no-broken-circuit basis of cohomology. This is based on the theory of wonderful embeddings and nested sets developed in [4]. Our result allows us to express the so-called Jeffrey-Kirwan residues in terms of integration on some explicit geometric cycles.

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