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

Abstract

In this paper, 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 and Vologodsky, cf. math.AG/0205117, and by Baranovsky and Ginzburg, cf. alg-geom/9607008.

20 pages. Final version. Improved exposition

References in corpus (2)

• Noncommutative tori and the Riemann-Hilbert correspondence
• La filtration canonique par les pentes d'un module aux q-différences et le gradué associé

Cited by in corpus (1)

• Confluence of meromorphic solutions of q-difference equations