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Titlebook: Lectures on p-adic Differential Equations; Bernard Dwork Book 1982 Springer-Verlag New York Inc. 1982 Equations.Hypergeometrische Differen

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,The , → ,′ Map,Let . ∈ ℚ ∩ ℤ., . ∈ (0, 1). We define .′ ∈ ℚ ∩ ℤ., by condition (3.7.0) with the restriction that ..
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Second-Order Linear Differential Equations Modulo Powers of ,None of the symbols concerning equation (2.4.5.1) will be used here. However, the notation of Chapter 5 will be of use.
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,Dieudonné Theory,Let . be a complete unramified extension of ℚ. with algebraically closed residue class field. Let . denote the Frobenius automorphism of . over ℚ.. Let . be a complete subfield of ., and let . (resp. .) be the ring of integers of . (resp. .)
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Abelian Differentials,The object of this chapter is to explain the meaning of the distinctions involving the relative magnitudes of ., ., and .. The notation here is that of Chapter 1 so the base field is Ω. = Q(.). We define . = . to be the Ω. space, ., of differentials of the form . with . ∈ .. We say that . ∈ . is exact if . for some . ∈ ..
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Supersingular Disks,We proceed to examine more carefully the canonical lifting . of Chapter 15. The hypotheses are those of that section and in particular . = 1. We will restrict our attention to the case Min(., .) > . but the extension to the case . > Max(., .) causes no difficulty. As before we write
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The Function , on Supersingular Disks (, = 1),In this section we continue the discussion of the matrix . of Lemma 16.5. We again restrict our attention to the case . = 1, Min(., .) > .. By minor modifications, the case . > Max(., .) may also be treated. As before . = ., . represents a supersingular disk.
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