Elliptic formal group laws, integral Hirzebruch genera and Krichever genera

Abstract

We consider the geometrical addition law on the elliptic curve in Tate coordinates. It corresponds to the general formal group law over the ring of polynomials with integer coefficients of the parametra of the curve. We study the structure of this law and the differential equation that determines its exponent. We describe a 5-parametric family of Hirzebruch genera with integer values on stably complex manifolds. We introduce the general Krichever genus, which is given by a generalized Baker-Akhiezer function. This function has many of the fundamental properties of the Baker-Akhiezer function, but unlike it, it is not meromorphic, because it can have two branch points in the parallelogram of periods.

arXiv comment39 pages

References in corpus (2)

• Spin generalization of the Ruijsenaars-Schneider model, non-abelian 2D Toda chain and representations of Sklyanin algebra
• Universal elliptic functions

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• Algebraic elliptic cohomology and flops II: $SL$-cobordism
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• Smooth Schubert varieties and generalized Schubert polynomials in algebraic cobordism of Grassmannians
• Algorithmic construction of Shimura - Taniyama - Weil parametrization of elliptic curves over the rationals