I have been fortunate to be accepted to some top ten programs and USC. My primary interests are Algebraic K-theory, Motives, A^1 homotopy theory and Algebraic Geometry. The real pickle is the Top 10 ten programs i have been admitted do not have any K-theorist and people directly studying these problems per say (not that I can see in their publications) but are fantastic Algebraic geometry schools. (Not U Chicago, Northwestern, UCLA and I did not apply to H,P, Berkley, and Stanford)

However I have also been admitted to USC which have two fantastic K-theorists namely Eric Freidlander and Aravind Asok whose work i really can relate to. The fact is it is not a top school. I am leaning towards this school primarily because I have spent the last whole year independently working on K-Theory and have a result which has been submitted to a good journal. I do not know if prestige should win over the choice of possible advisors. I would have to change my research focus to other aspects of Algebraic geometry if I choose to attend the Top end programs. Some serious words of advice would help. I enjoy geometry on the whole per say but Homotopical algebraic geometry and K theory really seems to be my focus currently. USC is close to UCLA another school with great research focus in my interest. My greed factor is USC allows me to do these things and I have enough time to think of some nicer problems.

My worries are will it really affect my career if I choose such a mid tier school? I know many variables are involved.

Also I did observe that a TOP school has only 2 algebraic geometers currently and last year had only 5 (3 pure + 2 applied) people joining the program. I am pretty keen about the program though I have not yet recieved a final word yet (waitlist sob story). 3 people in pure math joining the math phd program was rather disturbing to me. Also the place has one advisor choice per say (unless i choose to change research area under which I would very very easily choose the other top programs). Is it really worth awaiting such a small program? The nearest other big school is about 2 plus hours away.

Thanks