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The purpose of the present article is to initiate Arakelov theory of noncommutative arithmetic surfaces. Roughly speaking, a noncommutative arithmetic surface is a noncommutative projective scheme of cohomological dimension 1 of finite type over Spec ℤ. An important example is the category of...
We deal with homogeneous toric bundles M over generalized flag manifolds G C / P , where G is a compact semisimple Lie group and P a parabolic subgroup. Using symplectic data, we provide a simple characterization of the homogeneous toric bundles M which are Fano; we then show that a homogeneous...
In recent papers Honda, J. Diff. Geom 82: 411–444, 2009, Honda, Invent. Math 174, 463–504, 2008, we gave explicit description of some new Moishezon twistor spaces. In this paper, developing the method in the papers much further, we explicitly give projective models of a number of new...
We consider Frobenius algebras and their bimodules in certain abelian monoidal categories. In particular we study the Picard group of the category of bimodules over a Frobenius algebra, i.e. the group of isomorphism classes of invertible bimodules. The Rosenberg-Zelinsky sequence describes a...
Abstract We give a number of new characterizations of the Jiang–Su algebra 𝒵, both intrinsic and extrinsic, in terms of C *-algebraic, dynamical, topological and K -theoretic conditions. Along the way we study divisibility properties of C *-algebras, we give a precise characterization of...
To a definable subset of (or to a scheme of finite type over ℤ p ) one can associate a tree in a natural way. It is known that the corresponding Poincaré series ∑ N λ Z λ ∈ ℤ Z is rational, where N λ is the number of nodes of the tree at depth λ. This suggests that the trees...
A stability study of the correlations of multiplicative arithmetic functions yields necessary and sufficient conditions that the frequency distributions naturally attached to sums of additive arithmetic functions ƒ 1 ( n ) + ƒ 2 ( N – n ) on the integers not exceeding N possess a limiting...
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