Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An inverse theorem for the uniformity seminorms associated with the
  action of $F^\omega$   Let $\F$ a finite field. We show that the universal characteristic factor for
the Gowers-Host-Kra uniformity seminorm $U^k(\X)$ for an ergodic action
$(T_g)_{g \in \F^\omega}$ of the infinite abelian group $\F^\omega$ on a
probability space $X = (X,\B,\mu)$ is generated by phase polynomials $\phi: X
\to S^1$ of degree less than $C(k)$ on $X$, where $C(k)$ depends only on $k$.
In the case where $k \leq \charac(\F)$ we obtain the sharp result $C(k)=k$.
This is a finite field counterpart of an analogous result for $\Z$ by Host and
Kra. In a companion paper to this paper, we shall combine this result with a
correspondence principle to establish the inverse theorem for the Gowers norm
in finite fields in the high characteristic case $k \leq \charac(\F)$, with a
partial result in low characteristic.

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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
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The categories of this paper are: ao-sci
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The categories of this paper are: chao-dyn
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The categories of this paper are: supr-con
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The categories of this paper are: math-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg