Summary:
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.
Spanish layman's summary:
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.
English layman's summary:
This work presents algorithms which simplify expressions in the Grothendieck ring of Chow motives that involve its λ-ring structures, as well as Adams operations. The computation of motives of some moduli spaces is performed, allowing the computational verification of conjectural formulas for them.
Keywords: Lambda-rings; Symbolic computations of motives; Chow motives; Moduli spaces; Higgs bundles moduli space
JCR Impact Factor and WoS quartile: 0,700 - Q4 (2022)
DOI reference:
https://doi.org/10.1007/s00200-022-00558-3
Published on paper: December 2022.
Published on-line: June 2022.
Citation:
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, December 2022. [Online: June 2022]
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