<var>p</var>-adic motivic cohomology in arithmetic

  • Wiesława Nizioł

    University of Utah, Salt Lake City, United States
<var>p</var>-adic motivic cohomology in arithmetic cover
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We will discuss recent progress by many people in the program of representing motivic cohomology with torsion coefficients of arithmetic schemes by various arithmetic p-adic cohomologies: étale, logarithmic de Rham–Witt, and syntomic. To illustrate possible applications in arithmetic geometry we will sketch proofs of the absolute purity conjecture in étale cohomology and comparison theorems of p-adic Hodge theory.