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Showing 1 to 5 of 5 for “"Torsors"”.
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Torsors over Simplicial Schemes
… between the set of isomorphism classes of G-torsors over X, and the set of maps in the homotopy category of simplicial presheaves on C, with respect to the local weak equivalences, from X to BG. We prove basic results about the resulting non-abelian cohomology invariant, including an exact …
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Internal Yoneda Ext Groups, Central H-spaces, and Banded Types
… namely that of a banded type. The type of such torsors form a delooping of a central H-space, analogously to how the type of torsors of a group G form a K(G,1). Using centrality, we define a tensor product on banded types, producing an H-space structure which makes the type of torsors into a …
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Graded Lie Algebras, Compactified Jacobians and Arithmetic Statistics
… Wang. The main innovations are an analysis of torsors on affine spaces using results of Colliot--Thelene and the Grothendieck--Serre conjecture, a study of geometric properties of compactified Jacobians using the Białynicki-Birula decomposition, and a general construction of integral orbit …
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Computability of rational points on curves over function fields in characteristic p
… explicit equations defining Z/pZ- and [ mu]p-torsors over them. We prove an effective de Franchis-Severi theorem for characteristic p that generalizes the one given by Baker, et al. over number fields ([3]). Lastly, we use a height bound proved by Szpiro ([34]) to give an algorithm to compute Y …
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Langlands Duality in the Generic Fibres of Classical Hitchin Fibrations
… and GLn. Akin to Hitchin's result, the bres are torsors of abelian varieties, and we demonstrate Langlands duality in the Hitchin bration by proving the generic bres corresponding to Langland's dual groups are indeed dual abelian varieties. The thesis consists of two parts. In Part I, we review …