Adams operations and Galois structure
Copyright policy )Adams operations and Galois structure
We present a new method for determining the Galois module structure of the cohomology of coherent sheaves on varieties over the integers with a tame action of a finite group. This uses a novel Adams-Riemann-Roch type theorem obtained by combining the Kunneth formula with localization in equivariant K-theory and classical results about cyclotomic fields. As an application, we show two conjectures of Chinburg-Pappas-Taylor, in the case of curves.
30 pp, few additional changes
- Michigan State University United States
14C35, Mathematics - Number Theory, 14L30, 14F05, 19E08, Riemann–Roch theorem, 14C40, 11R33, Mathematics - Algebraic Geometry, 11S23, Galois cover, FOS: Mathematics, Galois module, Euler characteristic, Number Theory (math.NT), Algebraic Geometry (math.AG), 20C10
14C35, Mathematics - Number Theory, 14L30, 14F05, 19E08, Riemann–Roch theorem, 14C40, 11R33, Mathematics - Algebraic Geometry, 11S23, Galois cover, FOS: Mathematics, Galois module, Euler characteristic, Number Theory (math.NT), Algebraic Geometry (math.AG), 20C10
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