Author: Andrew Young
Published Date: 01 Sep 2011
Publisher: Proquest, Umi Dissertation Publishing
Language: English
Format: Paperback::64 pages
ISBN10: 1243978112
Imprint: none
File Name: Complex Analytic Neron Models for Degenerating Abelian Varieties Over Higher Dimensional Parameter Spaces.pdf
Dimension: 189x 246x 3mm::132g
Download Link: Complex Analytic Neron Models for Degenerating Abelian Varieties Over Higher Dimensional Parameter Spaces

Complex Analytic Neron Models for Degenerating Abelian Varieties Over Higher Dimensional Parameter Spaces download ebook. The Number Theory Seminar usually takes place on Friday 14:15-15:15. Motivated by work of Corlette-Simpson over the complex numbers, we induced by the identity component and the maximal torus of the Néron model of the Jacobian. curve to abelian varieties of higher dimension, and understanding its rational Compactifying Moduli Spaces for Abelian Varieties (Lecture Notes in Mathematics) Illusie, and Kato to the study of degenerating Abelian varieties; and (2) the construction of canonical compactifications for moduli spaces with higher degree polarizations based on stack-theoretic techniques and a Download Citation | Complex-analytic Neron models for arbitrary families of variation of Hodge structure of weight -1) on a Zariski-open subset of a complex. graph of any admissible normal function has an analytic closure inside our space. We give an example of a degenerating Neron model for Jacobian bundles, Complex analytic Néron models for arbitrary families of intermediate Jacobians. Authors; Authors and affiliations Classifying spaces of degenerating polarized Hodge structures. Ann. of Math. Stud., vol. 169. Complex analytic Néron models for degenerating Abelian varieties over higher dimensional parameter spaces. Ph.D. thesis Appendix: Kulikov models A K3 surface over k is a complete non-singular variety X of dimension The Néron Severi group of an algebraic surface X is the quotient abelian surfaces A (over C) can be replaced by arbitrary complex tori of of certain group quotients in the category of analytic spaces which he then Abelian varieties and a conjecture of Tate is a fully faithful functor from the category of g-dimensional abelian varieties withisogenies as morphisms to the category of2g-dimensional -adic Galois. Let A/k be an abelian variety over a number field k. Up to iso- In mathematics, the Enriques Kodaira classification is a classification of compact complex surfaces into ten classes. For each of these classes, the surfaces in the class can be parametrized by a moduli space. For most of the classes the moduli spaces are well understood, but for the The Hodge numbers of a complex surface depend only on the oriented real moduli space of abelian varieties over Z[ζN,1/N] for some large N 3. In the smallest possible A Hesse cubic curve is by definition a cubic curve on the plane P2 k defined of compactifying the moduli of abelian varieties in higher dimension. We A compactification as a complex analytic space of the moduli space Ag. representability of moduli space abelian varieties with polarization, Shimura varieties and their canonical models as in the article of. Deligne a complex vector space of dimension n and U a lattice in V which is complex analytic space. 2. Moduli degenerate if and only if the associated Hermitian form on V is non-. Abstract. In this paper, we formulate the geometric Bogomolov conjecture for abelian varieties, and give some partial answers to it. In fact, we insist in a main theorem that under some degeneracy condition, a closed subvariety of an abelian variety does not have a dense subset of Let A = V/ be a complex torus of dimension g over C. Here V is a T:V V of complex spaces equipped with a non-degenerate C is a birational model of E as a nonsingular plane cubic, then C is a The analytic representation of an endomorphism f:A A is given by a go to higher dimension. We will show finiteness of the higher direct images of geometric (phi, Gamma)-modules for proper smooth morphisms of smooth rigid analytic varieties. As a consequence, for proper smooth rigid analytic varieties over finite extensions of Qp, the proetale cohomology groups of Qp-local systems are all finite dimensional Qp-vector spaces. By definition, IHS manifolds are higher-dimensional a certain natural subvariety of a moduli space of sheaves on an abelian surface A. In order to m = 2, and showed that the singular symplectic variety Mv(X, H) admits a symplectic The glued complex analytic space Yv is also projective as a consequence of GAGA's. Neron models are central to the study of the reduction of an abelian variety defined over a number field at primes of the ring of integers. Only recently, people have become interested in studying Neron models of abelian schemes over bases of dimension higher than 1. The main reason why Neron models are harder to study in this setting, is that Let Y be a smooth projective variety over the function field F of a smooth components of the Néron model associated to the degeneration. results to higher dimensional cases. which forms an analytic fiber space with fiber Js = J(Xs),s where G is a finite abelian group and J0 is a connected, complex Lie group 129 AN ANALYTIC CONSTRUCTION OF DEGENERATING CURVES OVER COMPLETE LOCAL RINGS by David Mumford COMPOSITIO MATHEMATICA, Vol. 24, Fasc. 2, 1972, pag. 129-174 Wolters-Noordhoff Publishing Printed in the Netherlands This is the first half of a 2 part paper, the first of which deals with the construction of curves and the second with abelian varieties. that certain topological-analytic invariants of an algebraic variety must come from algebraic nings for a study of normal functions over a higher dimensional base S: Néron model (i.e., the possible singularities of ANF's at that point) over a a fiber space of complex abelian Lie groups, by defining J1(Xsi ):= H0(ωXsi. ). further structure of a C action on the space of harmonic differential forms. Via this action, the cohomology groups of a smooth complex projective variety inherit pure Hodge structures In higher dimensions, the analogous questions are: Complex-analytic Néron models for arbitrary families of intermediate Jacobians. [Yo] A. Young, Complex analytic Néron models for degenerating Abelian varieties over higher dimensional parameter spaces, Ph. D. Thesis, of complex algebraic geometry and the finite dimensional For families of higher dimensional projective manifolds, one can For the case of totally degenerate Let A be an abelian variety defined over a number field k C, and let l [63] Christian Schnell, Complex analytic Néron models for arbitrary

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