Abstract
Fix a fractional \({C_F}-{\rm ideal}\,\mathfrak{c}\supset {C_F}.\) In this chapter we introduce the linear algebraic 3 notions of c-polarized RM modules and c-polarized CM modules, and show that 4 certain spaces of special endomorphisms of these objects carry natural quadratic 5 forms. The modules themselves will reappear in Chap. 3 as the first homology of 6 abelian surfaces over C with real and complex multiplication, and the quadratic 7 spaces of special endomorphisms will underlie the the construction of Hilbert 8 modular Eisenstein series in Sect. 4.5.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Howard, B., Yang, T. (2012). Linear Algebra. In: Intersections of Hirzebruch–Zagier Divisors and CM Cycles. Lecture Notes in Mathematics(), vol 2041. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23979-3_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-23979-3_2
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-23978-6
Online ISBN: 978-3-642-23979-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)