The Hasse principle for bilinear symmetric forms over a ring of integers of a global function field
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In this article, it was shown that the set Cl ∞ ( O _ V ) of O { ∞ } -isomorphism classes in the genus of f of rank n > 2 is bijective as a pointed set to the abelian groups H et 2 ( O ∞, μ _ 2 ) ≅ Pic(C af ) / 2, i.e. it is an invariant of C af.About:
This article is published in Journal of Number Theory.The article was published on 2016-11-01 and is currently open access. It has received 6 citations till now. The article focuses on the topics: Ring of integers & Pointed set.read more
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On the classification of quadratic forms over an integral domain of a global function field
Rony A. Bitan,Rony A. Bitan +1 more
TL;DR: In this article, it was shown that the set of genera in the proper classification of quadratic O S -spaces isomorphic to (V, q ) in the flat or etale topology, is in 1 : 1 correspondence with Br 2 ( O S ), thus there are 2 | S | − 1 genera.
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On the flat cohomology of binary quadratic forms over $\mathbb{F}_q[x]$
TL;DR: In this article, the authors prove an analogue of Gauss' result for forms over the ring of rational functions, and express the full classification in terms of ''text{Pic}(\mathcal{O}_K)
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On the genera of semisimple groups defined over an integral domain of a global function field
TL;DR: In this article, a semisimple abelian group of rational functions over a smooth and projective curve is defined over a finite field, where the ring of regular functions on the curve is a Dedekind domain.
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The twisted forms of a semisimple group over a Hasse domain of a global function field
TL;DR: In this article, a semisimple and almost-simple group scheme is defined over a smooth fundamental group, and a finite set of twisted-forms of the group is described in terms of the Dynkin diagram.
References
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Book
Algebraic groups and number theory
TL;DR: Adeles and Ideles as discussed by the authors gave a generalization of the Strong Approximation Theorem for algebraic groups over locally compact fields and showed that the strong and weak approximations in algebraic numbers of groups are equivalent.
Book
Introduction to quadratic forms
TL;DR: In this paper, the authors present an abstract theory of quadratic forms over global fields with respect to the Dedekind axioms for S ideal theory of extension fields.
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Algebraic Geometry and Arithmetic Curves
TL;DR: In this paper, the authors present some topics in commutative algebra, including general properties of schemes, morphisms and base change, and local properties of sheaves of differentials.