منابع مشابه
Modular Curves and Rigid-analytic Spaces
1.1. Motivation. In the original work of Katz on p-adic modular forms [Kz], a key insight is the use of Lubin’s work on canonical subgroups in 1-parameter formal groups to define a relative theory of a “canonical subgroup” in p-adic families of elliptic curves whose reduction types are good but not too supersingular. The theory initiated by Katz has been refined in various directions (as in [AG...
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Let p be a prime > 3 and consider the Tate algebra A := Q p z defined to be the Banach algebra of formal power series over Q p that converge on the closed unit disk B[0, 1] ⊆ C p with the supremum norm ||f || := sup z∈B[0,1] |f (z)| for f ∈ A. Equivalently, we have (0.1) A = f (z) = ∞ k=0 a k z k a k ∈ Q p and lim k→∞ a k = 0 and the norm is given by (0.2) ||f || = sup k |a k |, for f = ∞ k=0 a...
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The paper serves as an introduction to etale cohomology of rigid analytic spaces. A number of basic results are proved, e.g. concerning cohomological dimension, base change, invariance for change of base elds, the homotopy axiom and comparison for etale cohomology of algebraic varieties. The methods are those of classical rigid analytic geometry and along the way a number of known results on ri...
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We evaluate a rigid analytical analogue of the Beilinson-Bloch-Deligne regulator on certain explicit elements in the K2 of Drinfeld modular curves, constructed from analogues of modular units, and relate its value to special values of L-series using the Rankin-Selberg method.
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The main goal of this article is to give an explicit rigid analytic uniformization of the maximal toric quotient of the Jacobian of a Shimura curve over Q at a prime dividing exactly the level. This result can be viewed as complementary to the classical theorem of Čerednik and Drinfeld which provides rigid analytic uniformizations at primes dividing the discriminant. As a corollary, we offer a ...
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ژورنال
عنوان ژورنال: Pure and Applied Mathematics Quarterly
سال: 2006
ISSN: 1558-8599,1558-8602
DOI: 10.4310/pamq.2006.v2.n1.a3