Arakelov motivic cohomology I

Details Arakelov motivic cohomology I Arakelov motivic cohomology I

2010-12-12

arxiv.org/abs/1012.2523v2

Mathematics

Number Theory

Scientific paper

This paper introduces a new cohomology theory for schemes of finite type over an arithmetic ring. The main motivation for this Arakelov-theoretic version of motivic cohomology is the conjecture on special values of $L$-functions and zeta functions formulated by the second author. Taking advantage of the six functors formalism in motivic stable homotopy theory, we establish a number of formal properties, including pullbacks for arbitrary morphisms, pushforwards for projective morphisms between regular schemes, localization sequences, $h$-descent. We round off the picture with a purity result and a higher arithmetic Riemann-Roch theorem. changes to first version: overhauled the definition of the Arakelov motivic cohomology spectrum, added a motivic and an arithmetic Riemann-Roch theorem

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