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We complete the calculations begun in Buzzard and Gee ( Int. Math. Res. Not. IMRN  12 (2009) 2303–2317), using the  p ‐adic local Langlands correspondence for GL 2 (ℚ  p  ) to give a complete description of the reduction modulo  p  of the 2‐dimensional crystalline representations ofG      pof slope less than 1, when  p  > 2.

Explicit reduction modulo p of certain 2‐dimensional crystalline representations, II