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Publications [#243407] of Robert Bryant
search www.ams.org.Papers Published
 with Bryant, RL; Griffiths, PA, Characteristic cohomology of differential systems. I. General theory,
The Journal of the American Mathematical Society, vol. 8 no. 3
(1995),
pp. 507507 [MR96c:58183], [dvi], [doi]
(last updated on 2017/12/12)
Author's Comments: This paper is the first of a series in which we explore
the relationship
between the geometry of a PDE (in the sense of
differential invariant theory)
and its socalled 'characteristic cohomology', a
generalization of the
notion of conservation laws that is largely due to
Vinogradov. Rather than
work directly with a PDE system, we work with the
associated exterior differential
system and formulate the theory in a way that is natural
in this context.
We develop some new commutative algebra tools to
help deal with the computations
that arise in our treatment of the spectral sequences
involved, and explore
the relationship between the characteristic variety of the
system and various
vanishing theorems that generalize the famous
Vinogradov 2line theorem.


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