Hodge Theory Seminar
Thursday, October 27, 2005, 4:30pm, 120 Physics
Andreas Rosenschon (SUNY Buffalo)
Rigidity

Abstract:

Let $F$ be a cohomology theory with torsion values which is defined for smooth schemes over fields. Given an extension $K/k$ of fields, we ask when one has rigidity in the sense that the map $F(X)\rightarrow F(X_K)$ is an isomorphism. For example, this is known to hold in case $K/k$ is an extension of algebraically closed fields, and $F$ is \'etale cohomology or algebraic $K$-theory (with coefficients). We prove the analogous result for other types of field extensions (not necessarily algebraically closed) in case $F$ belongs to a certain class of theories including, for example, algebraic $K$-theory, motivic cohomology, and \'etale cohomology (with finite coefficients). We outline how to prove a similar result for algebraic cobordism. This is joint work with {\O}stv{\ae}r.

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