Abstract:

We continue from last week by defining K_0 and K_1-regularity of a ring and prove that a regular ring is K_0 and K_1-regular. We show that distinguished squares of schemes give rise to an exact sequence relating their Picard groups and prove that K_0-regularity implies Pic-regularity. Then we define the Karoubi-Villamayor K-theory groups of a ring and relate
these to the K_0 and K_1 groups.

Further details: http://userpage.fu-berlin.de/hoskins/seminar.html [userpage.fu-berlin.de]