This article has three goals. First, we generalize the result of Deuring and Serre on the characterization of supersingular locus to all Shimura varieties given by totally indefinite quaternion algebras over totally real number fields. Second, we generalize the result of Ribet on arithmetic level raising to such Shimura varieties in the inert case. Third, as an application to number theory, we ...

Bloch points in permalloy cylinders are investigated using a micromagnetic framework, where thermal effects are included via the Landau-Lifshitz-Bloch equation of motion. We show that this enables micromagnetic modeling of a Bloch point avoiding the problem of singularities, which have been rep0l1ed in the literature so far. The details of the Bloch point which we reveal are compared with earli...

Especially notable here is Spencer Bloch’s semi-regularity paper [B]. The advantage of this approach is that one can use the full strength of the deformation theory of subvarieties. One might similarly ask whether there is a family of algebraic cycles {Zt}t∈B deforming Z; some first steps toward an infinitesimal theory for this problem were the subject of [G-G2]. A third possible context, which...

SUMMARY This paper presents a methodology for designing single-degree-of-freedom expandable " free-form " structures composed of rigid blocks connected through simple cylindrical joints. The underlying idea is to interconnect two or more individually expandable plate structures. Using a two-dimensionally expanding sphere as a first example, the conditions that must be satisfied to preserve the ...

The characterization by weighted Lipschitz continuity is given for the Bloch space on the unit ball of Rn. Similar results are obtained for little Bloch and Besov spaces.

We construct an example of a torus T over a field K for which the Galois symbol K(K;T, T )/nK(K; T, T ) → H(K,T [n] ⊗ T [n]) is not injective for some n. Here K(K; T, T ) is the Milnor K-group attached to T introduced by Somekawa. We show also that the motive M(T×T ) gives a counterexample to another generalization of the Milnor-BlochKato conjecture (proposed by Beilinson).

Strategic market games model strategic exchange economies as noncooperative simultaneous moves games. A recent paper by Bloch and Ghosal (J. Econ. Theory, 74 (1997), 368{384.) has shown that strategic market games might exhibit a rather counterintuitive comparative statics property: an increase in the number of traders on the own side of the market might increase the equilibrium utility for any...

This is a sequel to [FJ]. It will give a more natural framework for constructing elements in the Hopf algebra χF of framed mixed Tate motives according to Bloch and Křiž [BK]. This framework allows us to extend the results of [FJ] to interpret all multiple zeta values (including the divergent ones) and the multiple polylogarithms in one variable as elements of χF . It implies that the pro-unipo...

We study point-sphere and point-plane incidences in three-dimensional space. In particular, for 1 < k < n, we say that a set of spheres (resp., planes) is k-non-degenerate if no circle is contained in k spheres of the set (resp., if no line is contained in k planes of the set). We prove that, for every ε > 0, the number of incidences between a set of m points and a k-non-degenerate set of n sph...

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