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We give a new proof of Bradens theorem ([Br]) about emph{hyperbolic restrictions} of constructible sheaves/D-modules. The main geometric ingredient in the proof is a 1-parameter family that degenerates a given scheme Z equipped with a G_m-action to the product of the attractor and repeller loci.
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Let G be the Tate module of a p-divisble group H over a perfect field k of characteristic p. A theorem of Scholze-Weinstein describes G (and therefore H itself) in terms of the Dieudonne module of H; more precisely, it describes G(C) for good semiperfect k-algebras C (which is enough to reconstruct G). In these notes we give a self-contained proof of this theorem and explain the relation with the classical descriptions of the Dieudonne functor from Dieudonne modules to p-divisible groups.
The main purpose of this paper is to make Nakayamas theorem more accessible. We give a proof of Nakayamas theorem based on the negative definiteness of intersection matrices of exceptional curves. In this paper, we treat Nakayamas theorem on algebraic varieties over any algebraically closed field of arbitrary characteristic although Nakayamas original statement is formulated for complex analytic spaces.
In this note I provide two extensions of a particular case of the classical Poncelet theorem.
This paper discusses a central theorem in birational geometry first proved by Eugenio Bertini in 1891. J.L. Coolidge described the main ideas behind Bertinis proof, but he attributed the theorem to Clebsch. He did so owing to a short note that Felix Klein appended to the republication of Bertinis article in 1894. The precise circumstances that led to Kleins intervention can be easily reconstructed from letters Klein exchanged with Max Noether, who was then completing work on the lengthy report he and Alexander Brill published on the history of algebraic functions [Brill/Noether 1894]. This correspondence sheds new light on Noethers deep concerns about the importance of this report in substantiating his own priority rights and larger intellectual legacy.
On a complex symplectic manifold we prove a finiteness result for the global sections of solutions of holonomic DQ-modules in two cases: (a) by assuming that there exists a Poisson compactification (b) in the algebraic case. This extends our previous results in which the symplectic manifold was compact. The main tool is a finiteness theorem for R-constructible sheaves on a real analytic manifold in a non proper situation.
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