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Algebraic versus Rigid Cohomology with Logarithmic
Abelian Varieties from the Rigid Analytic Viewpoint
Witt Realization of pAdic BarsottiTate Groups
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A-module A-number of F abelian variety affine space Algebraic Geometry algebraically closed Barsotti Barsotti-Tate group bialgebra bivector canonical characteristic closed subscheme coefficients cohomology complex components computes the A-number Corollary corresponding crystalline cohomology defined denote dense open set Dieudonne dimension dual element elliptic curve embedded lifting etale exact sequence exists fibre finite field finite flat group finite type flat group schemes formal formula Frobenius group schemes homomorphism hypersurface implies inclusion integer irreducible isomorphism Lemma Li(x line bundle linear form lisse log schemes log structure logarithmic Math mixed of weight moduli space monoids morphism multiplicative Newton polygon notation oo-slopes open set p-adic parameter perverse sheaf polynomial prime number Proof Proposition prove pure of weight quotient resp Rham ring semi-stable reduction semiperverse sheaf sheaves smooth subset supersingular Suppose Theorem theory topology trivial vanishes Witt vectors zero