Geometry of Loop Eisenstein Series
نویسنده
چکیده
Part 3. Geometric Construction of Loop Eisenstein Series 31 11. Bloch’s Map 31 12. Adeleic Loop groups and G-bundles on a Punctured Surface 33 13. Affine flag varieties and extensions of G-bundles 38 14. Relative Chern classes and Central extensions 41 15. Loop Eisenstein Series and Geometric Generating Functions 47 16. Ribbons and a Formal Analogue 48 17. Example: Loop Eisenstein Series on P1. 53
منابع مشابه
Derivatives of Eisenstein Series andArithmetic Geometry*
We describe connections between the Fourier coefficients of derivatives of Eisenstein series and invariants from the arithmetic geometry of the Shimura varieties M associated to rational quadratic forms (V,Q) of signature (n, 2). In the case n = 1, we define generating series φ̂1(τ ) for 1-cycles (resp. φ̂2(τ ) for 0-cycles) on the arithmetic surface M associated to a Shimura curve over Q. These ...
متن کاملStandard compact periods for Eisenstein series
When o has larger class number, linear combinations of CM-point values corresponding to the ideal classes yield the corresponding ratio. This example was understood in the 19th century, and is the simplest in well-known families of special values and periods of Eisenstein series. The next case in order of increasing complexity is that of integrals of the same Es along hyperbolic geodesics in H ...
متن کاملEisenstein Series in String Theory
We discuss the relevance of Eisenstein series for representing certain G(Z)-invariant string theory amplitudes which receive corrections from BPS states only. The Eisenstein series are constructed using G(Z)-invariant mass formulae and are manifestly invariant modular functions on the symmetric space K\G(R) of noncompact type, with K the maximal compact subgroup of G(R). In particular, we show ...
متن کاملOn the Derivative of an Eisenstein Series of Weight One
In [17], a certain family of Siegel Eisenstein series of genus g and weight (g + 1)/2 was introduced. They have an odd functional equation and hence have a natural zero at their center of symmetry (s = 0). It was suggested that the derivatives at s = 0 of such series, which we will refer to as incoherent Eisenstein series, should have some connection with arithmetical algebraic geometry. Some e...
متن کاملModular forms and arithmetic geometry
The aim of these notes is to describe some examples of modular forms whose Fourier coefficients involve quantities from arithmetical algebraic geometry. At the moment, no general theory of such forms exists, but the examples suggest that they should be viewed as a kind of arithmetic analogue of theta series and that there should be an arithmetic Siegel–Weil formula relating suitable averages of...
متن کامل