Simplification of λ-ring expressions in the Grothendieck ring of Chow motives

D. Alfaya

Applicable Algebra in Engineering, Communication and Computing Vol. 33, nº. 6, pp. 599 - 628

Resumen:

The Grothendieck ring of Chow motives admits two natural opposite λ-ring structures, one of which is a special structure allowing the definition of Adams operations on the ring. In this work I present algorithms which allow an effective simplification of expressions that involve both λ-ring structures, as well as Adams operations. In particular, these algorithms allow the symbolic simplification of algebraic expressions in the sub-λ-ring of motives generated by a finite set of curves into polynomial expressions in a small set of motivic generators. As a consequence, the explicit computation of motives of some moduli spaces is performed, allowing the computational verification of some conjectural formulas for these spaces.

Resumen divulgativo:

Este trabajo presenta algoritmos que simplifican expresiones en el anillo de Grothendieck de motivos de Chow que involucran sus estructuras de λ-anillo y operaciones de Adams. Se calculan los motivos de algunos espacios de moduli, verificando computacionalmente fórmulas conjeturales para ellos. 

Palabras Clave: Lambda-rings; Symbolic computations of motives; Chow motives; Moduli spaces; Higgs bundles moduli space

Índice de impacto JCR y cuartil WoS: 0,700 - Q4 (2022); 0,600 - Q4 (2023)

Referencia DOI: https://doi.org/10.1007/s00200-022-00558-3

Publicado en papel: Diciembre 2022.

Publicado on-line: Junio 2022.

Cita:
D. Alfaya, Simplification of λ-ring expressions in the Grothendieck ring of Chow motives. Applicable Algebra in Engineering, Communication and Computing. Vol. 33, nº. 6, pp. 599 - 628, Diciembre 2022. [Online: Junio 2022]