E-Dissertationen: Browsing E-Dissertationen by Author "Rapoport, Michael"
Now showing items 1-12 of 12
-
Affine Grassmannians and Geometric Satake Equivalences
Richarz, Timo (2014-02-18)The work deals with the geometric Satake equivalence. A new proof is given in the case of a split connected reductive group. Further the work extends the ramified geometric Satake equivalence from tamely ramified groups ... -
Complex Multiplication, Rationality and Mirror Symmetry for Abelian Varieties and K3 Surfaces
Chen, Meng (2007)This thesis consists of three parts. In the first part we study abelian varieties and K3 surfaces of CM-type (i.e. their Hodge group is commutative), aiming at a characterization of complex multiplication via the existence ... -
Construction of a Rapoport-Zink space for split GU(1, 1) in the ramified 2-adic case
Kirch, Daniel Leonhard (2016-07-06)Let F be a finite extension over the field of 2-adic numbers. In this paper, we construct a Rapoport-Zink-space for the split unitary group in two variables over a ramified quadratic extension of F. For this, we first ... -
The delta invariant in Arakelov geometry
Wilms, Robert (2016-05-24)In this thesis we study Faltings' delta invariant of compact and connected Riemann surfaces.
This invariant plays a crucial role in Arakelov theory of arithmetic surfaces. For example, it appears in the arithmetic ... -
Intersections of arithmetic Hirzebruch-Zagier cycles
Terstiege, Ulrich (2009-06-15)We establish a close connection between the intersection multiplicities of three arithmetic Hirzebruch-Zagier cycles and the Fourier coefficients of the derivative of a certain Siegel-Eisenstein series. Our main result ... -
Local L(2)-Cohomology of Shimura Varieties
Meusers, Volker (2008)We give a new proof of Zuckers Conjecture relating the intersection cohomology of a locally symmetric variety to its L2-cohomology. This is achieved using techniques developed by Jens Franke in his proof of the Borel conjecture. -
On affine Deligne-Lusztig varieties for GLn
Mierendorff, Eva (2005)In the first part of this thesis we study the global structure of moduli spaces of quasi-isogenies of p-divisible groups introduced by Rapoport and Zink. We determine their dimensions and their sets of connected components ... -
On arithmetic families of filtered φ-modules and crystalline representations
Hellmann, Eugen (2011-05-10)We consider stacks of filtered phi-modules over rigid analytic and adic spaces. We show that these modules parametrize p-adic Galois representations of the absolute Galois group of a p-adic field with varying coefficients ... -
Perfectoid spaces
Scholze, Peter (2012-03-09)We introduce a certain class of so-called perfectoid rings and spaces, which give a natural framework for Faltings' almost purity theorem, and for which there is a natural tilting operation which exchanges characteristic ... -
Relative unitary RZ-spaces and the Arithmetic Fundamental Lemma
Mihatsch, Andreas Johannes (2017-03-29)We verify new cases of the Arithmetic Fundamental Lemma (AFL) of Wei Zhang. This relies on a recursive algorithm which allows, under certain conditions, to reduce the AFL identity in question to an AFL identity in lower ... -
Stability conditions on derived categories
Meinhardt, Sven (2008)My thesis is divided into two parts. In the first part I consider stability conditions on the derived category of complex manifolds without any nontrivial subvarieties. In particular, I construct and classify stability ...
-
The supersingular locus of the Shimura variety of GU(1,s)
Vollaard, Inken-Kareen (2005)In this paper I study the supersingular locus of the reduction modulo p of the Shimura variety of GU(1,s) in the case of an inert prime p. Using Dieudonné theory I define a stratification of the ...