Galois Action on Homology of the Heisenberg Curve

Aristides Kontogeorgis; Dimitrios Noulas

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arXiv · 2411.11140

Galois Action on Homology of the Heisenberg Curve

Aristides Kontogeorgis·Dimitrios Noulas

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Abstract

The Heisenberg curve is defined topologically as a cover of the Fermat curve and corresponds to an extension of the projective line minus three points by the non-abelian Heisenberg group modulo n. We compute its fundamental group and investigate an action from Artin's Braid group to the curve itself and its homology. We also provide a description of the homology in terms of irreducible representations of the Heisenberg group over a field of characteristic $0$.

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Aristides Kontogeorgis, Dimitrios Noulas. 2024-11-17. Galois Action on Homology of the Heisenberg Curve. https://arxiv.org/abs/2411.11140

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