?? "multiplicative group of k[x]/x^2=5" (for example ...) as algebraic group .... ?? to what extent and in what context we've thought about stuff like that recently ... ?? .... ?? part of "alg comm ring" bit ?? .... ?? ...... ??? ..... ?? in part hoped to relate zeta function to l-function ... ??? ..... ??? .....

?? asking this now because of reading bump .... ??? .... "unsplit torus" ... algebraic group over f_q that "splits" to give torus over f_[q^n] ... ?? more abstractly, alg gp over z ..... ????? ...... ???? .....

?? confusion here about ... ??? naive size count ..... ??? .... (q-1)^n vs q^n-1 .... ???? ......

?? gaussian integers .... ???? ..... reciprocity law .... splitting pattern .... ???? ..... ???? .... ???? .... counting solutions ....

?? counting homomorphisms from gaussian integers, vs counting dimension of space of homomorphisms from .... ???? "formal gaussian integers" .... ???? ..... ????? ...... ?????? ....... ????? ...... zeta vs l .... ????? .... ???? ....... ???? .....

?? studying reps of gl(2,f_q) .... "unsplit torus" intrudes .... ??? .... gl(1,f_[q^2]) -> gl(2,f_q) .... ???? ....

??? studying reps of gl(2,z) ... ??? gl(1,z[i]) -> gl(2,z) ...... ???? ..... ???? .....

?? gl(1,z[i]) -> gl(2,z) as algebraic stabilizer subgroup of what structure on what stuff ??? ..... ???? ... hmmm .... ??? stuff here as "2d object" ???? ..... ???? .... stabilized structure as .... ????? ......

vs gl(1,z^2) -> gl(2,z) .... ????? ...... ???? .... ?? "splitting" ... ??? bit about "complex splitting" / "complex idempotent" .... ??? .... ?? .... ??? level slip ??? .... ??? ..... ???? ...... "splitting" here as "generic flag-pair" ??? .... ???? ..... ????? ..... ?? "twisted splitting" ??? ..... ???? .....

???? "lattice" ???? ...... ???? .... "extra dot" .... ???? brown vs pressley and segal .... ???? ......