Local analytic classification of $q$-difference equations with $\lvert q \rvert= 1$

Lucia Di Vizio

doi:10.4171/jncg/33

JournalsjncgVol. 3, No. 1pp. 125–149

Local analytic classification of $q$ -difference equations with $∣ q ∣ = 1$

Lucia Di Vizio
Institut de Mathématiques de Jussieu
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Abstract

In this article, we establish, under convenient diophantine assumptions, a complete analytic classification of $q$ -difference modules over the field of germs of meromorphic functions at zero, proving some analytic analogs of the results by Soibelman–Vologodsky and by Baranovsky–Ginzburg.

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Lucia Di Vizio, Local analytic classification of $q$ -difference equations with $∣ q ∣ = 1$ . J. Noncommut. Geom. 3 (2009), no. 1, pp. 125–149

DOI 10.4171/JNCG/33