Abstract
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.
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Acknowledgements
I would like to thank André Oliveira for useful discussions.
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This research was funded by MICINN Grant PID2019-108936GB-C21.
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Alfaya, D. Simplification of λ-ring expressions in the Grothendieck ring of Chow motives. AAECC 33, 599–628 (2022). https://doi.org/10.1007/s00200-022-00558-3
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DOI: https://doi.org/10.1007/s00200-022-00558-3