344 research outputs found

    On a Conjecture of Rapoport and Zink

    Full text link
    In their book Rapoport and Zink constructed rigid analytic period spaces FwaF^{wa} for Fontaine's filtered isocrystals, and period morphisms from PEL moduli spaces of pp-divisible groups to some of these period spaces. They conjectured the existence of an \'etale bijective morphism FaFwaF^a \to F^{wa} of rigid analytic spaces and of a universal local system of QpQ_p-vector spaces on FaF^a. For Hodge-Tate weights n1n-1 and nn we construct in this article an intrinsic Berkovich open subspace F0F^0 of FwaF^{wa} and the universal local system on F0F^0. We conjecture that the rigid-analytic space associated with F0F^0 is the maximal possible FaF^a, and that F0F^0 is connected. We give evidence for these conjectures and we show that for those period spaces possessing PEL period morphisms, F0F^0 equals the image of the period morphism. Then our local system is the rational Tate module of the universal pp-divisible group and enjoys additional functoriality properties. We show that only in exceptional cases F0F^0 equals all of FwaF^{wa} and when the Shimura group is GLnGL_n we determine all these cases.Comment: v2: 48 pages; many new results added, v3: final version that will appear in Inventiones Mathematica

    The Particle Spectrum of Heterotic Compactifications

    Get PDF
    Techniques are presented for computing the cohomology of stable, holomorphic vector bundles over elliptically fibered Calabi-Yau threefolds. These cohomology groups explicitly determine the spectrum of the low energy, four-dimensional theory. Generic points in vector bundle moduli space manifest an identical spectrum. However, it is shown that on subsets of moduli space of co-dimension one or higher, the spectrum can abruptly jump to many different values. Both analytic and numerical data illustrating this phenomenon are presented. This result opens the possibility of tunneling or phase transitions between different particle spectra in the same heterotic compactification. In the course of this discussion, a classification of SU(5) GUT theories within a specific context is presented.Comment: 77 pages, 3 figure
    corecore