Duke Mathematical Journal
- Duke Math. J.
- Volume 147, Number 3 (2009), 541-575.
Stark-Heegner points and the cohomology of quaternionic Shimura varieties
Let be a totally real field of narrow class number one, and let be a modular, semistable elliptic curve of conductor . Let be a non-CM quadratic extension with such that the sign in the functional equation of is . Suppose further that there is a prime that is inert in . We describe a -adic construction of points on which we conjecture to be rational over ring class fields of and satisfy a Shimura reciprocity law. These points are expected to behave like classical Heegner points and can be viewed as new instances of the Stark-Heegner point construction of . The key idea in our construction is a reinterpretation of Darmon's theory of modular symbols and mixed period integrals in terms of group cohomology
Duke Math. J. Volume 147, Number 3 (2009), 541-575.
First available in Project Euclid: 1 April 2009
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14G05: Rational points
Secondary: 14G35: Modular and Shimura varieties [See also 11F41, 11F46, 11G18]
Greenberg, Matthew. Stark-Heegner points and the cohomology of quaternionic Shimura varieties. Duke Math. J. 147 (2009), no. 3, 541--575. doi:10.1215/00127094-2009-017. https://projecteuclid.org/euclid.dmj/1238592865