26th International Conference on Applications of Computer Algebra - ACA 2021, Waterloo (Canada) Online. 23-27 July 2021
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
Publication date: 2021-07-23.
Citation:
D. Alfaya, Simplification of λ-ring expressions in the Grothendieck ring of Chow motives, 26th International Conference on Applications of Computer Algebra - ACA 2021, Waterloo (Canada) Online. 23-27 July 2021.
