Results 11 to 20 of about 40,053 (26)

Common Slots of Bilinear and Quadratic Pfister Forms

, 2018
We show that over any field $F$ of $\operatorname{char}(F)=2$ and 2-rank $n$, there exist $2^n$ bilinear $n$-fold Pfister forms that have no slot in common. This answers a question of Becher's in the negative.
Chapman, Adam
core   +1 more source

Witt kernels and Brauer kernels for quartic extensions in characteristic two [PDF]

, 2014
Let $F$ be a field of characteristic $2$ and let $E/F$ be a field extension of degree $4$. We determine the kernel $W_q(E/F)$ of the restriction map $W_qF\to W_qE$ between the Witt groups of nondegenerate quadratic forms over $F$ and over $E$, completing
Hoffmann, Detlev W., Sobiech, Marco
core   +1 more source

Kato-Milne Cohomology and Polynomial Forms

, 2018
Given a prime number $p$, a field $F$ with $\operatorname{char}(F)=p$ and a positive integer $n$, we study the class-preserving modifications of Kato-Milne classes of decomposable differential forms.
Chapman, Adam, McKinnie, Kelly
core   +1 more source

Generalised quadratic forms and the u-invariant [PDF]

, 2017
The u-invariant of a field is the supremum of the dimensions of anisotropic quadratic forms over the field. We define corresponding u-invariants for hermitian and generalised quadratic forms over a division algebra with involution in characteristic 2 and
Dolphin, Andrew
core   +2 more sources

Koszul Complexes and Symmetric Forms over the Punctured Affine Space [PDF]

, 2017
Let X be a regular separated scheme of finite Krull dimension and let $U^{n}_{X} \subset A^{n}_{X}$ be the punctured affine n-space over X. We show that the total graded Witt ring of $U^{n}_{X}$ is a free graded module over the total graded Witt ring of ...
Balmer, Paul, Gille, Stefan
core  

Annihilating polynomials of excellent quadratic forms [PDF]

, 2018
.: If φ is an excellent form, then it is possible to use the dimensions of the higher complements of φ to obtain an annihilating polynomial of φ of low degree.
Rühl, Klaas-Tido
core  

Vector bundles of rank four and A_3 = D_3

, 2012
Over a scheme with 2 invertible, we show that a vector bundle of rank four has a sub or quotient line bundle if and only if the canonical symmetric bilinear form on its exterior square has a lagrangian subspace.
Asher Auel, Atiyah, Balmer, Balmer, Balmer, Balmer, Balmer, Bichsel, Bourbaki, Bruns, Calmès, Demazure, Demazure, Elman, Fasel, Fasel, Fasel, Fasel, Fulton, Gille, Grothendieck, Hartshorne, Hassett, Knebusch, Knus, Knus, Milne, Morel, Mumford, Parimala, Quebbemann, Quebbemann, Roy   +32 more
core   +1 more source

Morava K-theory of twisted flag varieties [PDF]

, 2014
In the present article we prove some results about the Morava K-theory. In particular, we construct an operation from the Morava K-theory to the Chow theory analogous to the second Chern class for Grothendieck's K0-theory.
Petrov, Victor, Semenov, Nikita
core  

Descent properties of hermitian Witt groups in inseparable extensions [PDF]

, 2018
Let k be a field of characteristic ≠ 2, A be a central simple algebra with involution σ over k and W(A, σ) be the associated Witt group of hermitian forms.
Bayer-Fluckiger, Eva, Moldovan, Daniel
core  

Weakly Hyperbolic Involutions

, 2018
Pfister's Local-Global Principle states that a quadratic form over a (formally) real field is weakly hyperbolic (i.e. represents a torsion element in the Witt ring) if and only if its total signature is zero.
Bayer-Fluckiger, Bernauer, Dejaiffe, Graham, Jacobson, Karim Johannes Becher, Karpenko, Knus, Lam, Lewis, Lewis, Lewis, Lewis, Parimala, Pfister, Quéguiner, Scharlau, Scharlau, Thomas Unger, Tignol   +19 more
core   +1 more source