## Report 32/2006: Algebraic $$K$$-Theory (July 16th – July 22nd, 2006).(English)Zbl 1109.19300

Abstract: This is the report on the Oberwolfach workshop Algebraic $$K$$-Theory, held in July 2006. The talks covered mainly topics from Algebraic Geometry and Number Theory in connection with $$K$$-Theory. Special emphasis was placed on motivic cohomology and motivic homotopy of general schemes.
Contributions:
Thomas Geisser, Duality via cycle complexes (p. 1945)
Florian Ivorra, l-adic realization of triangulated motives over a noetherian separated scheme and a motivic equivalence (p. 1947)
Hélène Esnault (joint with Phùng Hô Hai and Xiaotao Sun), On Nori’s fundamental group scheme (p. 1950)
Christian Haesemeyer (joint with G. Cortiñas and C. Weibel), K-theory of singularities and a conjecture of Vorst (p. 1952)
Joël Riou, Operations on algebraic K-theory and regulators via the homotopy theory of schemes (p. 1954)
Andreas Rosenschon (joint with V. Srinivas), Algebraic cycles on products of elliptic curves over p-adic fields (p. 1957)
Kanetomo Sato (joint with Shuji Saito), Weak Bloch-Beilinson conjecture for zero-cycles over p-adic fields (p. 1959)
Frédéric Déglise, Triangulated mixed motives and the 6 functors formalism (p. 1961)
Teena Gerhardt, On $$RO(S^1)$$-graded TR (p. 1963)
Clark Barwick, $$\mathcal D$$-crystals (p. 1966)
Hourong Qin, Reflection theorems and the $$p$$-Sylow subgroup of $$K_{2n}O_F$$ for a number field $$F$$ (p. 1969)
Jens Hornbostel (joint with Serge Yagunov), Rigidity for $$A^1$$-representable theories (p. 1971)
Rob de Jeu (joint with Amnon Besser, Paul Buckingham and Xavier- François Roblot), On the $$p$$-adic Beilinson conjecture for number fields (p. 1973)
Moritz Kerz, The Gersten conjecture for Milnor K-theory (p. 1976)
Baptiste Calmès (joint with Jens Hornbostel), Transfers for Witt groups and Grothendieck duality (p. 1978)
Paul Arne Østvær (joint with Oliver Röndigs), Modules over motivic cohomology (p. 1979)
Spencer Bloch, Algebraic cycles and additive Chow groups (p. 1981)
Stephen Lichtenbaum, Weil-étale cohomology of mixed motives (p. 1985)

### MSC:

 19Dxx Higher algebraic $$K$$-theory 19Exx $$K$$-theory in geometry 19Fxx $$K$$-theory in number theory 00B05 Collections of abstracts of lectures
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