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On the geometry of deformation rings and the Taylor-Wiles hypothesis

By Patrick Allen

Appears in collection : Galois Representations, Automorphic Forms and L-Functions / Représentations galoisiennes, formes automorphes et leurs fonctions L

We investigate the geometry of Galois deformation rings in the defect zero setting but when the Taylor-Wiles hypothesis does not hold. In particular, we consider the question of whether or not the map from the local deformation ring to the global deformation ring is a local complete intersection map and the role the Taylor-Wiles hypothesis plays in this question. We exhibit an example in the context of classical weight two modular forms where this does not hold and shows that a resulting Tor algebra acts on the cohomology of a modular orbifold. This is joint work in progress with Preston Wake.

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  • DOI 10.24350/CIRM.V.19934603
  • Cite this video Allen Patrick (6/21/22). On the geometry of deformation rings and the Taylor-Wiles hypothesis. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19934603
  • URL https://dx.doi.org/10.24350/CIRM.V.19934603

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