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A Representation of the 1st-Order Variational Sequence
in Field Theory

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*Jana Kašparová (Krpcová)*

**E-mail:** Jana.Kasparova@math.slu.cz
**Abstract.** Variational sequence of order $r$ introduced by Krupka
is defined on the $r$-jet prolongation of a fibered manifold $\pi :Y\rightarrow
X$, as a quotient sequence of the de Rham sequence of sheaves. In this
paper we describe explicitly the elements of the 1st-order variational
sequence over an $n$-dimensional manifold $X$.

**AMSclassification.** 58E99, 58A12, 58A15, 58A20

**Keywords.** Fibered manifold, contact form, strongly contact form,
trace decomposition problem, $q$-equation, sheaf, variational sequence