E-Dissertationen: Browsing E-Dissertationen by Author "Faltings, Gerd"
Now showing items 1-13 of 13
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Coherent sheaves with parabolic structure and construction of Hecke eigensheaves for some ramified local systems
Heinloth, Jochen (2003)The aim of these notes is to generalize Laumon's construction [18] of automorphic sheaves corresponding to local systems on a smooth, projective curve C to the case of local systems with indecomposable unipotent ramification ... -
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 ... -
Cycleclasses for algebraic De Rham cohomology and crystalline cohomology
Ring, Nicholas (2002)For schemes which are smooth over a regular base scheme we establish the existence of cycle class maps with values in the corresponding algebraic De Rham cohomology. These maps have all the properties one expects, i.e. ... -
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. <br /> This invariant plays a crucial role in Arakelov theory of arithmetic surfaces. For example, it appears in the arithmetic ... -
Galois cohomology of Fontaine rings
Lodh, Rémi Shankar (2007)Let $V$ be a complete discrete valuation ring of mixed characteristic. We express the crystalline cohomology of the special fibre of certain smooth affine $V$-schemes $X=Spec(R)$ tensored with an appropriate ring of $p$-adic ... -
Motivic Fundamental Groups and Integral Points
Hadian-Jazi, Majid (2010-07-16)We give a motivic proof of finiteness of S-integral points on punctured projective line. We do this by studying torsors over different notions of unipotent fundamental groups attached to an open curve defined over a number ... -
New Approach to Arakelov Geometry
Durov, Nikolai (2007)This work is dedicated to a new completely algebraic approach to Arakelov geometry, which doesn't require the variety under consideration to be generically smooth or projective. In order to construct such an approach we ... -
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 ... -
On GIT Compactified Jacobians via Relatively Complete Models and Logarithmic Geometry
Bellardini, Alberto (2014-07-09)In this thesis we study modular compactifications of Jacobian varieties attached to nodal curves.<br /> Unlike the case of smooth curves, where the Jacobians are canonical, modular compact objects, these compactifications ... -
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 ... -
Théorie de Bruhat-Tits, grassmanniennes affines et modèles locaux
Pereira Lourenço, João Nuno (2020-10-02)Nous développons la théorie de Bruhat-Tits pour les groupes quasi-réductifs sur les corps discrètement valués, henséliens et excellents, qui se quasi-déploient sur l'henselisé strict. Ensuite, cette théorie est appliquée ...