학술논문
A local analogue of the ghost conjecture of Bergdall-Pollack
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Working Paper
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Abstract
We formulate a local analogue of the ghost conjecture of Bergdall and Pollack, which essentially relies purely on the representation theory of GL_2(Q_p). We further study the combinatorial properties of the ghost series as well as its Newton polygon, in particular, giving a characterization of the vertices of the Newton polygon and proving an integrality result of the slopes. In a forthcoming sequel, we will prove this local ghost conjecture under some mild hypothesis and give arithmetic applications.
Comment: We change several notations from the first version. We change 'weak arithmetic module' to 'K_p-projective augmented module' in Definition 2.3 and change 'arithmetic p-adic forms' to 'abstract p-adic forms' in section 2.4. We also add an example (5.13) to explain the meaning of the function \Delta defined in 5.1
Comment: We change several notations from the first version. We change 'weak arithmetic module' to 'K_p-projective augmented module' in Definition 2.3 and change 'arithmetic p-adic forms' to 'abstract p-adic forms' in section 2.4. We also add an example (5.13) to explain the meaning of the function \Delta defined in 5.1