Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
Results
Showing 1 to 16 of 16 for “"Hodge theory"”.
-
HodgeRank: Applying Combinatorial Hodge Theory to Sports Ranking
… this thesis, we examine a ranking method called HodgeRank. HodgeRank was introduced in 2008 by Jiang, Lim, Yao and Ye as ``a promising tool for the statistical analysis of ranking, especially for datasets with cardinal, incomplete, and imbalanced information.'' To apply these methods, we require …
-
Equivariance in Tannakian duality and plectic p-adic Hodge theory
… We then study a plectic variant of Fontaine theory for p-adic representations of the local plectic Galois group at p associated to a totally real number field F, when p is inert in F. In particular, we show that the plectic crystalline Fontaine functor is valued in a category of plectic …
-
Analogues of Kähler geometry on Sasakian manifolds
… over a compact Kähler manifold, the results of Hodge theory in the Kahler case apply to basic forms on S. Even in the absence of a Kähler base, there is a basic version of Hodge theory due to El Kacimi-Alaoui. These results are useful in trying to imitate Kähler geometry on Sasakian manifolds; …
-
Harmonic forms under metric and topological perturbations
… examples illustrating various aspects of Hodge theory on Riemannian manifolds. We consider the relationship between the harmonic forms on a product space and the harmonic forms on the factors as well as the harmonic forms on a connected sum and the harmonic forms on the summands. Algebraic …
-
Asymptotically cylindrical Calabi–Yau and special Lagrangian geometry
… problem, we also consider an extension of Hodge theory to general asymptotically cylindrical manifolds. For our study of asymptotically cylindrical Calabi–Yau manifolds, we restrict to complex dimension three. We regard a Calabi–Yau structure as a pair of closed forms ($\Omega$, $\omega$); …
-
Higher direct images of ideal sheaves, correspondences in log Hodge cohomology and globally F-full varieties
… extends some foundational results in the theory of rational pairs that were previously known only in characteristic 0. Chapter 2 discusses correspondences in logarithmic Hodge theory related to an as-of-yet-unsuccessful alternative strategy for proving the main theorems of Chapter 1. …
-
On the slope filtration of [phi]-modules over the Robba ring
… results are expected to intervene in the duality theory for Selmer groups associated to de Rham representations. We introduce the notion of families of [phi]-modules which arises naturally from both rigid cohomology and p-adic Hodge theory. We then prove the local constancy of generic HN-polygons …
-
Odd dimensional symplectic manifolds by Zhenqi He.
… manifolds. In the first half we study the Hodge theory on the basic symplectic manifolds. We can define two cohomology theories on them, the standard basic de Rham cohomology gheory and a basic version of the Koszul-Brylinski-Mathieu 'harmonic' symplectic cohomology theory. Among our main …
-
Multiplicative Global Springer Theory
… areas, such as mirror symmetry, non-abelian Hodge theory and the geometric Langlands program. They are also useful for globalizing representation-theoretic phenomena such as Springer theory and the study of Springer fibers. In the local and global settings, Springer fibers are replaced by …
-
Cohomologically proper stacks over Zp̳ : algebra, geometry and representation theory
… featuring in particular recently developed theory of prismatic co-homology and the classical Deligne-Illusie method for the Hodge-to-de Rham degeneration. As main applications we prove the Totaro's conjectural inequality between the dimensions of the de Rham and the singular F[subscript …
-
The overconvergent de Rham-Witt complex
… first, we reinterpret several rings from p-adic Hodge theory in such a way that they admit analogues which use big Witt vectors instead of p-typical Witt vectors. In this generalization we check that several familiar properties continue to be valid. In the second, we offer a proof that the …
-
The Navier-Stokes equations for elliptic quasicomplexes
… of the de Rham complex. In particular, the Hodge theory for the de Rham complex enables one to eliminate the pressure from the equations. The Navier-Stokes equations constitute a parabolic system with a nonlinear term which makes sense only for one-forms. A simpler model of dynamics of …
-
The topology of terminal quartic 3-folds
… been studied in the context of Mixed Hodge Theory. I have tackled it from the point of view of Mori theory. I use birational geometric methods to obtain these results.
-
Iwasawa theory for modular forms at supersingular primes
… We begin by studying the p-adic Hodge theory for the p-adic representation associated to f in the case when a_p=0. It allows us to give analogous definitions of Kobayashi's \pm-Coleman maps and \pm-Selmer groups. The Coleman maps are used to show that the Pontryagin duals of these …
-
The Plectic Weight Filtration on Cohomology of Shimura Varieties and Partial Frobenius
We prove that there is a natural plectic weight filtration on the cohomology of Hilbert modular varieties in the spirit of Nekov\'a\v r and Scholl. This is achieved with the help of Morel's work on weight t-structures and a detailed study of partial Frobenius. We prove in particular that the …
-
Components of the Emerton-Gee Moduli Stack of Galois Representations for GL2 and A Graph-Theoretic Approach to Computing Selmer Groups of Elliptic Curves over Q(i)
Let K be a finite unramified extension of Q_p with p ≥ 5. In the first part of this thesis, we study the local geometry of the irreducible components in the reduced part of the Emerton–Gee stack for GL_2, which serves as a moduli space for two-dimensional mod p representations of Gal(K/K). We …