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- W1520320358 abstract "This chapter describes a p -Adic inner product on elliptic modular forms. It presents a cohomology class in the first crystalline cohomology group. It is not true however that the map is always an injection. It is found that if F is an eigenform with complex multiplication such that its eigenvalue has valuation 1, it can be shown that the image is zero. This will follow from the theorem as the q invariant of the p -divisible group of an ordinary CM elliptic curve is a root of unity. It is not known whether this map is an injection when restricted to new forms or equivalently whether the inner product is nondegenerate when restricted to new forms. If W is assumed to be a basic wide open and y be a minimal underlying affinoid of W , W is a rigid space isomorphic to a complete curve C with good reduction X minus an affinoid, which after a finite etale base extension becomes a finite nonzero disjoint union of closed disks lieing in distinct residue classes of C ." @default.
- W1520320358 created "2016-06-24" @default.
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- W1520320358 date "1994-01-01" @default.
- W1520320358 modified "2023-09-25" @default.
- W1520320358 title "A p-Adic Inner Product on Elliptic Modular Forms" @default.
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- W1520320358 doi "https://doi.org/10.1016/b978-0-12-197270-7.50010-3" @default.
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