Results 1 to 10 of about 40,053 (26)

Grothendieck–Serre in the quasi-split unramified case

Forum of Mathematics, Pi, 2022
The Grothendieck–Serre conjecture predicts that every generically trivial torsor under a reductive group scheme G over a regular local ring R is trivial. We settle it in the case when G is quasi-split and R is unramified.
Kęstutis Česnavičius
doaj   +1 more source

Witt groups of Severi-Brauer varieties and of function fields of conics [PDF]

Épijournal de Géométrie Algébrique
The Witt group of skew hermitian forms over a division algebra $D$ with symplectic involution is shown to be canonically isomorphic to the Witt group of symmetric bilinear forms over the Severi-Brauer variety of $D$ with values in a suitable line bundle.
Anne Quéguiner-Mathieu, Jean-Pierre Tignol   +1 more
doaj   +1 more source

Chain Equivalences for Symplectic Bases, Quadratic Forms and Tensor Products of Quaternion Algebras [PDF]

, 2014
We present a set of generators for the symplectic group which is different from the well-known set of transvections, from which the chain equivalence for quadratic forms in characteristic 2 is an immediate result.
Chapman, Adam
core   +1 more source

Witt kernels of quadratic forms for multiquadratic extensions in characteristic 2 [PDF]

, 2014
Let $F$ be a field of characteristic $2$ and let $K/F$ be a purely inseparable extension of exponent $1$. We show that the extension is excellent for quadratic forms. Using the excellence we recover and extend results by Aravire and Laghribi who computed
Hoffmann, Detlev W.
core   +1 more source

Annihilating polynomials for quadratic forms

International Journal of Mathematics and Mathematical Sciences, Volume 27, Issue 7, Page 449-455, 2001., 2001
This is a short survey of the main known results concerning annihilating polynomials for the Witt ring of quadratic forms over a field.
David W. Lewis
wiley   +1 more source

Springer's theorem for tame quadratic forms over Henselian fields [PDF]

, 2010
A quadratic form over a Henselian-valued field of arbitrary residue characteristic is tame if it becomes hyperbolic over a tamely ramified extension. The Witt group of tame quadratic forms is shown to be canonically isomorphic to the Witt group of graded
Elomary, Mohamed Abdou, Tignol, Jean-Pierre   +1 more
core   +2 more sources

Trivial Witt groups of flag varieties

, 2011
Let G be a split semi-simple linear algebraic group over a field, let P be a parabolic subgroup and let L be a line bundle on the projective homogeneous variety G/P.
Baptiste Calmès, Demazure, Jean Fasel, Merkurjev   +3 more
core   +2 more sources

Differential forms, linked fields, and the u-invariant [PDF]

, 2017
We associate an Albert form to any pair of cyclic algebras of prime degree p over a field F with char(F) = p which coincides with the classical Albert form when p = 2. We prove that if every Albert form is isotropic, then H-4(F) = 0.
Chapman, Adam, Dolphin, Andrew
core   +3 more sources

An analogue of the Milnor conjecture for the de Rham-Witt complex in characteristic 2

Forum of Mathematics, Sigma
We describe the modulo $2$ de Rham-Witt complex of a field of characteristic $2$ , in terms of the powers of the augmentation ideal of the $\mathbb {Z}/2$ -geometric fixed points of real topological restriction homology ${\mathrm ...
Emanuele Dotto
doaj   +1 more source

Linkage of Pfister forms over $\mathbb{C}(x_1,\ldots,x_n)$

, 2019
In this note, we prove the existence of a set of $n$-fold Pfister forms of cardinality $2^n$ over $\mathbb{C}(x_1,\dots,x_n)$ which do not share a common $(n-1)$-fold factor. This gives a negative answer to a question raised by Becher. The main tools are
Chapman, Adam, Tignol, Jean-Pierre
core   +1 more source