Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Duality of Drinfeld modules and $\wp$-adic properties of Drinfeld
  modular forms   Let $p$ be a rational prime and $q$ a power of $p$. Let $\wp$ be a monic
irreducible polynomial of degree $d$ in $\mathbf{F}_q[t]$. In this paper, we
define an analogue of the Hodge-Tate map which is suitable for the study of
Drinfeld modules over $\mathbf{F}_q[t]$ and, using it, develop a geometric
theory of $\wp$-adic Drinfeld modular forms similar to Katz's theory in the
case of elliptic modular forms. In particular, we show that for Drinfeld
modular forms with congruent Fourier coefficients at $\infty$ modulo $\wp^n$,
their weights are also congruent modulo $(q^d-1)p^{\lceil \log_p(n)\rceil}$,
and that Drinfeld modular forms of level $\Gamma_1(\mathfrak{n})\cap
\Gamma_0(\wp)$, weight $k$ and type $m$ are $\wp$-adic Drinfeld modular forms
for any tame level $\mathfrak{n}$ with a prime factor of degree prime to $q-1$.

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The categories of this paper are: gr-qc
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The categories of this paper are: physics
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The categories of this paper are: cond-mat
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The categories of this paper are: quant-ph
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The categories of this paper are: q-bio
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The categories of this paper are: cs
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: nlin
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The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
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The categories of this paper are: plasm-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org