Convolution, duality, and twist morphisms relate etale cohomology of local shtuka moduli spaces, yielding new proofs of the Kottwitz conjecture for GL_3 minuscule weights and GL_2 cuspidal parameters, plus counterexamples in non-minuscule cases.
Dat, Th\' e orie de L ubin- T ate non-ab\' e lienne et repr\' e sentations elliptiques, Invent
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Convolution morphisms and Kottwitz conjecture
Convolution, duality, and twist morphisms relate etale cohomology of local shtuka moduli spaces, yielding new proofs of the Kottwitz conjecture for GL_3 minuscule weights and GL_2 cuspidal parameters, plus counterexamples in non-minuscule cases.