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Showing 1 to 20 of 26 for “"Positive characteristic"”.
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Equivariant quantum connections in positive characteristic
… to study the equivariant quantum connections in positive characteristic. The main examples of interest arise from symplectic resolutions. We introduce equivariant generalizations of the quantum Steenrod operations of Fukaya, provide nontrivial computations in the example of the cotangent bundle …
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Representations of Cherednik algebras in positive characteristic
… of the rational Cherednik algebras of rank 1 in characteristic p > 0. There are two cases. One is the "quantum" case, where "Planck's constant" is nonzero and generic irreducible representations have dimension pr, where r is the order of the cyclic group contained in the algebra. The other is the …
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Tamely ramified geometric Langlands correspondence in positive characteristic
… ramified geometric Langlands correspondence in positive characteristic for GLn(k), where k is an algebraically closed field of characteristic p > n. Let X be a smooth projective curve over k with marked points, and fix a parabolic subgroup of GLn(k) at each marked point. We denote by Bun(n,P) …
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Deligne categories and representation stability in positive characteristic
… representation theory of symmetric groups Sn, in positive characteristic as n grows to [infinity], with the goal of understanding and generalizing the Deligne categories Rep(St) as well as the theory of FI-modules and representation stability in the positive characteristic setting. We also give …
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Quantum geometric Langlands correspondence in positive characteristic: the GLN case
… > 1 over an algebraically closed field k of characteristic p > 0, and c [epsilon] k \ Fp. Let BunN be the stack of rank N vector bundles on C and Ldet the line bundle on BunN given by determinant of derived global sections. In this thesis, we construct an equivalence of derived categories of …
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Iterative Differential Galois Theory in Positive Characteristic: A Model Theoretic Approach
… of Kolchin's differential Galois theory to positive characteristic iterative differential fields, generalizing to the non-linear case the iterative Picard-Vessiot theory recently developed by Matzat and van der Put. Instead of taking an algebraic approach, we use the methods and framework …
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Two problems in the theory of curves over fields of positive characteristic
This thesis consists of two parts. In the first half, we define, so called, generalized Artin-Schreier cover of a scheme X over k. After defining Artin-Schreier group scheme Γ over X, a generalized Artin-Schreier cover is realized as a principal homogeneous space of Γ. We are especially interested …
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Limit linear series in positive characteristic and Frobenius-unstable vector bundles on curves
(cont.) yield a new proof of a result of Mochizuki yield a new proof of a result of Mochizuki Frobenius-unstable bundles for C general, and hence obtaining a self-contained proof of the resulting formula for the degree of V₂.
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On the center of the ring of invariant differential operators on semisimple groups over fields of positive characteristic
DSpace SAF Submission Ingestion Package generated from Vireo submission #11707 on 2018-03-13 at 10:08:13
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Classification of all parabolic subgroup schemes of a semisimple linear algebraic group over an algebraically closed field of positive characteristic
Given a semisimple linear algebraic group G over an algebraically closed field K, we fix a Borel subgroup B and a maximal torus T. This determines a root system $\Phi$, and a set of simple roots $\Delta$. The subgroups containing B are called parabolic subgroups. They correspond to subsets of …
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Simple Lie algebras and their classification
… give the complete classification over a field of characteristic zero. In Chapter 6 we discuss the notion ofChevalley basis which is important for the definition of classical Lie algebras over a field of positive characteristic. We end up in Chapter 7 with providing the basic notions about the …
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The Frobenius direct image of line bundles and the structure of representations
… theory of semisimple algebraic groups in positive characteristic, the induced line bundles, ${\cal L}$($\lambda$), on the flag variety G/B, are important objects of study. E.g., their global sections form representations of G which are dual to the Weyl modules. In this thesis, our central …
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Arithmetic and dynamical systems
… approximation problems in local �fields of positive characteristic, one a generalisation of the Khintchine{Groshev theorem, another a central limit theorem. We also prove a P�olya{Carlson dichotomy result for a large class of adelicly perturbed rational functions. In particular we prove that …
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Higher direct images of ideal sheaves, correspondences in log Hodge cohomology and globally F-full varieties
… of) birational morphisms of pairs in arbitrary characteristic, and as an application 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 …
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On Berglund-Hübsch-Krawitz Mirror Symmetry
… both over the complex numbers and fields of positive characteristic. Finally, we provide a conjectural framework that unifies the toric mirror construction of Batyrev and Borisov with the BHK construction in the context of Kontsevich's Homological Mirror Symmetry Conjecture.
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Iterative Connections and Abhyankar's Conjecture
… unifies the theory of modules with connection in characteristic zero as given by N. Katz and the theory of iterative differential modules in positive characteristic as given by B. H. Matzat und M. van der Put. The second part of this work is about the differential Abhyankar conjecture for …
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The representation theory of diagram algebras
… The representation theory of these algebras in characteristic zero is well understood, and we show that it can be described through the action of a reflection group on the set of simple modules (a result previously known for the Temperley-Lieb and Brauer algebras). By considering the action of …
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Algebraic geometry and representation theory in the Verlinde category
… categories over algebraically closed fields of positive characteristic. A specific focus is paid to the Verlinde category, a symmetric fusion category in characteristic p that serves as a universal base for all such categories. Symmetric tensor categories provide a natural setting in which it …
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Combinatorial Methods in the Representation Theory of the Symmetric Group
… are the Specht modules, which over fields of characteristic 0 are a complete set of simple modules. These can be defined combinatorially and thus allow an explicit combinatorial approach to be taken to their study. This dissertation, as with the modern study of the representation theory of the …
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