290 research outputs found
Non-surjectivity of the Clifford invariant map
No full textThe question whether there exists a commutative ring A for which there is an element in the 2-torsion of the Brauer group not represented by a Clifford algebra was raised by Alex Hahn. Such an example is constructed in this paper and is arrived at using certain results of Parimala-Sridharan and Parimala-Scharlau which are also reviewed here
Erratum for “Galois algebras, Hasse principle and induction-restriction methods” (vol 16, pg 677, 2011)
No full textThis is a correction to [BP 11] E. Bayer-Fluckiger, R. Parimala, Galois algebras, Hasse principle and induction-restriction methods, Documenta Math. 16 (2011), 677-707.CSA
Trace forms of G-Galois algebras in virtual cohomological dimension 1 and 2
No full textLet G be a finite group and let k be a field of char(k) not equal 2. We explicitly describe the set of trace forms of G-Galois algebras over k when the virtual 2-cohomological dimension vcd(2)(k) of k is at most 1. For fields with vcd(2)(k) less than or equal to 2 we give a cohomological criterion for the orthogonal sum of a trace form of a G-Galois algebra with itself to be isomorphic to another such form
From Mennicke symbols to Euler Class groups
No full textBhatwadekar and Raja Sridharan have constructed a homomorphism from an orbit set of unimodular rows to an Euler class group. We show under weaker assumptions that a generalization of its kernel is a subgroup. Our tool is a partially defined operation on the set of unimodular matrices with two rows
R-equivalence in adjoint classical groups over fields of virtual cohomological dimension
No full textLet F be a field of characteristic not 2 whose virtual cohomological dimension is at most 2. Let G be a semisimple group of adjoint type defined over F. Let RG(F) denote the normal subgroup of G(F) consisting of elements R-equivalent to identity. We show that if G is of classical type not containing a factor of type Dn, G(F)/RG(F)= 0. If is a simple classical adjoint group of type Dn, we show that if F and its multi-quadratic extensions satisfy strong approximation property, then G(F)/RG(F)= 0. This leads to a new proof of the R-triviality of F-rational points of adjoint classical groups defined over number fields
Quadratic Counts of Twisted Cubics
No full textUsing a quadratic version of the Bott residue theorem, we give a quadratic
refinement of the count of twisted cubic curves on hypersurfaces and complete
intersections in a projective space.Comment: thanks to J.C. Ottem and R. Parimala that were inadvertently omitted
in the first version were added to the introductio
Quadratic spaces over Laurent extensions of Dedekind domains
No full textLet R be a Dedekind domain in which 2 is invertible. We show in this paper that any isotropic quadratic space over R[T, T-1] is isometric to q1⊥ Tq2 where q1, q2 are quadratic spaces over . We give an example to show that this result does not hold for anisotropic spaces
R.: On compositions and triality
No full textDedicated with gratitude to Professor K. Chandrasekharan on his 80 th birthda
Nonextended quadratic forms over polynomial rings over power series rings
No full textIf R is a complete discrete valuation ring, then every quadratic space over R[T] is extended from R. We here show by an example that a corresponding result for higher-dimensional complete regular local rings is not valid
On generalized quaternion algebras
No full textLet B be a commutative ring with 1, and G(={σ}) an automorphism group of B of order 2. The generalized quaternion ring extension B[j] over B is defined by S. Parimala and R. Sridharan such that (1) B[j] is a free B-module with a basis {1,j}, and (2) j2=−1 and jb=σ(b)j for each b in B. The purpose of this paper is to study the separability of B[j]. The separable extension of B[j] over B is characterized in terms of the trace (=1+σ) of B over the subring of fixed elements under σ. Also, the characterization of a Galois extension of a commutative ring given by Parimala and Sridharan is improved
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