On the splitting of quasilinear p-forms
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Stephen Scully
Abstract
Using an analogue of Knebusch's generic splitting tower invariant in the theory of non-singular quadratic forms, we study the splitting behaviour of quasilinear (or Fermat-type) forms of degree p over fields of characteristic p > 0. Several new applications of our main results to the theory of quasilinear quadratic forms are provided, including an analogue of a theorem of Vishik relating to the existence of outer excellent connections in the motives of smooth projective quadrics over fields of characteristic different from 2, partial results towards a quasilinear version of Karpenko's theorem on the possible values of the first higher Witt indices of non-singular quadratic forms in characteristic not 2, and a proof of a conjecture of Hoffmann concerning quadratic forms with maximal splitting in the quasilinear case.
Funding source: University of Nottingham
Award Identifier / Grant number: doctoral training grant
Funding source: London Mathematical Society, Cecil King Memorial Foundation
Award Identifier / Grant number: Cecil King Travel Scholarship
This work was carried out as part of my Ph.D. thesis at the University of Nottingham, and I would like to thank my advisors, Detlev Hoffmann and Alexander Vishik, for numerous helpful discussions. The final version of the paper was partly written during a three-month visit to the University of California, Los Angeles, and I gratefully acknowledge the support of the London Mathematical Society and Cecil King Memorial Foundation which made this visit possible.
© 2016 by De Gruyter
Articles in the same Issue
- Frontmatter
- Congruence kernels around affine curves
- On the dynamical and arithmetic degrees of rational self-maps of algebraic varieties
- On the splitting of quasilinear p-forms
- Graded quiver varieties and derived categories
- On the limit of spectral measures associated to a test configuration of a polarized Kähler manifold
- Static Klein–Gordon–Maxwell–Proca systems in 4-dimensional closed manifolds. II
- Linear stability of algebraic Ricci solitons
- Dynamical stability of algebraic Ricci solitons
- Erratum to Dynamics of the Krichever construction in several variables (J. reine angew. Math. 572 (2004), 111–138)
- Addendum: The case of closed surfaces (Boundary value problems on planar graphs and flat surfaces with integer cone singularities I: The Dirichlet problem)
Articles in the same Issue
- Frontmatter
- Congruence kernels around affine curves
- On the dynamical and arithmetic degrees of rational self-maps of algebraic varieties
- On the splitting of quasilinear p-forms
- Graded quiver varieties and derived categories
- On the limit of spectral measures associated to a test configuration of a polarized Kähler manifold
- Static Klein–Gordon–Maxwell–Proca systems in 4-dimensional closed manifolds. II
- Linear stability of algebraic Ricci solitons
- Dynamical stability of algebraic Ricci solitons
- Erratum to Dynamics of the Krichever construction in several variables (J. reine angew. Math. 572 (2004), 111–138)
- Addendum: The case of closed surfaces (Boundary value problems on planar graphs and flat surfaces with integer cone singularities I: The Dirichlet problem)
