On the p-adic cohomology of the Lubin-Tate tower

By Peter Scholze. 2015

97 citations recorded by the source corpus.

We prove a finiteness result for the p-adic cohomology of the Lubin-Tate tower. For any n>=1 and p-adic field F, this provides a canonical functor from admissible p-adic representations of GL_n(F) towards admissible p-adic representations of Gal_F x D^*, where Gal_F is the absolute Galois group of F, and D/F is the central division algebra of invariant 1/n. Moreover, we verify a local-global-compatibility statement for this correspondence, and compatibility with the patching construction of Caraiani-Emerton-Gee-Geraghty-Paskunas-Shin.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/26220de9feda2b31bf94d2a9168e9adc5fd03231

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In Geometry and Topology

1. T. Gee
2. J. Thorne
3. Peter Scholze
4. Frank Calegari
5. Ana Caraiani
6. James Newton
7. P. Allen
8. David Geraghty

In Mathematical Physics

1. T. Gee
2. J. Thorne
3. Peter Scholze
4. Frank Calegari
5. Ana Caraiani
6. James Newton
7. P. Allen
8. David Geraghty

Citations in the corpus

• Potential automorphy over CM fields (2018, methodology): “We find it convenient to use the language of ultrafilters here, following [Sch15a] and [GN16].”