Admissibility of groups over function fields of p-adic curves

Reddy, B. Surendranath; Suresh, V.

doi:10.1016/j.aim.2012.12.017

Cited by 18 publications

(10 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(b) In the presence of sufficiently many roots of unity, a valuation analog of the first assertion in Theorem 9.12 can also be shown, again by drawing on [HHK09, Theorem 5.1]. See Theorem 2.6 of [RS13].…”

Section: Applications To Central Simple Algebrasmentioning

confidence: 91%

Local-global principles for torsors over arithmetic curves

Harbater¹,

Hartmann²,

Krashen³

2015

ajm

104

View full text Add to dashboard Cite

We consider local-global principles for torsors under linear algebraic groups, over function fields of curves over complete discretely valued fields. The obstruction to such a principle is a version of the Tate-Shafarevich group; and for groups with rational components, we compute it explicitly and show that it is finite. This yields necessary and sufficient conditions for local-global principles to hold. Our results rely on first obtaining a Mayer-Vietoris sequence for Galois cohomology and then showing that torsors can be patched. We also give new applications to quadratic forms and central simple algebras.

show abstract

Section: Applications To Central Simple Algebrasmentioning

confidence: 91%

Local-global principles for torsors over arithmetic curves

Harbater¹,

Hartmann²,

Krashen³

2015

ajm

104

View full text Add to dashboard Cite

show abstract

“…By Merkurjev-Suslin theorem, there is a quadratic form p α of trivial discriminant such that e 2 (p α ) = α. By [RS,Theorem 2.6], there exists a non-trivial discrete valuation v such that ind(α ⊗ F v ) = 2 n . Let L/F be a quadratic extension which is split over v. Let p be the norm form of L/F .…”

Section: Lower Bounds For Splitting Dimensionmentioning

confidence: 99%

Generalized period-index problem with an application to quadratic forms

Gosavi¹

2019

Preprint

View full text Add to dashboard Cite

Let F be the function field of a curve over a complete discretely valued field. Let ℓ be a prime not equal to the characteristic of the residue field. Given a finite subgroup B in the ℓ torsion part of the Brauer group ℓ Br(F ), we define the index of B as the minimum of the degrees of field extensions which split all elements in B. In this manuscript, we give an upper bound for the index of any finite subgroup B in terms of arithmetic invariants of F . As a simple application of our result, given a quadratic form q/F , where F is the function field of a curve over an n-local field, we provide an upper bound to the minimum of degrees of field extensions L/F so that the Witt index of q ⊗ L becomes the largest possible.

show abstract

“…The following proposition is proved in [RS13, 2.4] under the assumption that contains a primitive th root of unity.…”

Section: Brauer Group: Complete Two-dimensional Regular Local Ringsmentioning

confidence: 99%

Local–global principle for reduced norms over function fields of -adic curves

Parimala¹,

Preeti²,

Suresh³

2017

Compositio Math.

Self Cite

View full text Add to dashboard Cite

Abstract. Let F be the function field of a p-adic curve. Let D be a central simple algebra over F of period n and λ ∈ F * . We show that if n is coprime to p and D · (λ) = 0 in H 3 (F, µ ⊗2 n ), then λ is a reduced norm. This leads to a Hasse principle for the SL 1 (D), namely an element λ ∈ F * is a reduced norm from D if and only if it is a reduced norm locally at all discrete valuations of F .

show abstract

Admissibility of groups over function fields of p-adic curves

Cited by 18 publications

References 16 publications

Local-global principles for torsors over arithmetic curves

Local-global principles for torsors over arithmetic curves

Generalized period-index problem with an application to quadratic forms

Local–global principle for reduced norms over function fields of -adic curves

Contact Info

Product

Resources

About