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Quadratic Forms, Linear Algebraic Groups, and Cohomology

Part of the Developments in Mathematics Book Series (volume 18)

Editors: Colliot-Thélène, Jean-Louis; Garibaldi, Skip; Sujatha, R.; Suresh, Venapally

DOI: 10.1007/978-1-4419-6211-9

ISBN: 978-1-4419-6210-2

Publisher: Springer New York - Springer Journals

Jun 11, 2010

1 - 10 of 22 Chapters

LitStream

Multiples of forms

Bayer-Fluckiger, Eva

Pages: 3 –11

[The aim of this paper is to survey and extend some results concerning multiples of (quadratic, hermitian, bilinear…) forms.]
LitStream

On Saltman’s p-Adic Curves Papers

Brussel, Eric

Pages: 13 –39

[We present a synthesis of Saltman’s work (Adv. Math. 43(3):250–283, 1982; J. Alg. 314(2):817–843, 2007) on the division algebras of prime-to-p degree over the function field K of a p-adic curve. Suppose Δ is a K-division algebra. We prove that (a) Δ’s degree divides the square of its period; (b)...
LitStream

Serre’s Conjecture II: A Survey

Gille, Philippe

Pages: 41 –56

[We provide a survey of Serre’s conjecture II (1962) on the vanishing of Galois cohomology for simply connected semisimple groups defined over a field of cohomological dimension at most 2.]
LitStream

Field Patching, Factorization, and Local–Global Principles

Krashen, Daniel

Pages: 57 –82

[The method of field patching has proven useful in obtaining results on Galois theory, central simple algebras, and quadratic forms. A crucial ingredient for this was proving certain “factorization” results for connected, rational linear algebraic groups. In this paper, we explore other possible...
LitStream

Deformation Theory and Rational Points on Rationally Connected Varieties

Lieblich, Max

Pages: 83 –108

[We give an account of some recent work on the existence of rational points on varieties over function fields, starting with basic material on deformation theory and the bend-and-break theorem. We emphasize the connection with the geometry of moduli spaces and include a sketch of the...
LitStream

Recent Progress on the Kato Conjecture

Saito, Shuji

Pages: 109 –124

[This is a survey paper on recent works in progress by Jannsen, Kerz, and the author on the Kato conjecture on the cohomological Hasse principle.]
LitStream

Elliptic Curves and Iwasawa’s µ = 0 Conjecture

Sujatha, R.

Pages: 125 –135

[The µ-invariant is a fundamental invariant in Iwasawa theory and a long-standing conjecture of Iwasawa asserts that it is zero for number fields. This can be viewed as a statement on an arithmetic Iwasawa module associated to the trivial motive. In this chapter, we discuss what the analogous...
LitStream

Cohomological Invariants of Central Simple Algebras with Involution

Tignol, Jean-Pierre

Pages: 137 –171

[This survey reviews the various invariants with values in Galois cohomology groups that have been defined for involutions on central simple algebras following the model of the discriminant, Clifford invariant, and Arason invariant of quadratic forms. From the orthogonal case to the unitary case...
LitStream

Witt Groups of Varieties and the Purity Problem

Zainoulline, Kirill

Pages: 173 –185

[We provide a general algorithm used to prove purity for functors with transfers. As a basic example we consider the Witt group of an algebraic variety.]
LitStream

Some Extensions and Applications of the Eisenstein Irreducibility Criterion

Bishnoi, Anuj; Khanduja, Sudesh K.

Pages: 189 –197

[Some generalizations of the classical Eisenstein and Schönemann Irreducibility Criteria and their applications are described. In particular some extensions of the Ehrenfeucht–Tverberg irreducibility theorem which states that a difference polynomial f(x) – g(y) in two variables is irreducible...

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