langlands

stuff that baez has been telling me about.... ??os... asf os... ???

???sa.... "eisenstein series" .... ???sa as related to mellin transform of hasse-weil zeta fn of "affine k-space + 1" ... ???os??? .... asf os... ???......

???but wa sa automorphic form ct automorphic rep here????? os???? ..... asf os... ????.....

??bump p 4... ???says will develop functional equation for dirichlet character... os... ??sounds like should explain sa automorphic rep corresponding to 1d galois rep ???? os???? ..... asf os.... ???......

??so wa this general zeta / general theta stuff here???? os???..... asf os... ????.....

??so what _is_ going on here?? sa "theta fn as modular form" os??? w_a_ sa different variables.... ??and different dimensions of qfs?? ... ??os??? ..... asf os... ????...... ???.....

p 9.... 1.14 and 1.15 ..... ???try to understand???.......

???also sa 1.16 (os... asf os...) and sa "ramification at -1" ??? os... asf os... ???.....

???1.14 as saying sa... ??yes just use dirichlet coefficients as maclaurin coefficients??? os??? or sa maclaurin ct fourier os????..... asf os ... ???.....

???no wait it's very different from that??? ???sa "theta" .... quadratic... ???so what's going on here??? doesn't it seem like there's just 2 completely weirdly different patterns for 1d galois reps ct 2d ???? os????? ...... hmmmmm....... ????.....

????wa sa "g ct s" here??? os??? ..... gl(1) ct sl(2) .... ????os??? .... asf os... ???.....

???1.15 as saying sa automorphicness under something like reciprocal ... ????os????..... asf os... ???....

??so wa sa langlands correspondence for galois rep comeing from a number field?? ??os???....
asf os... ???sa getting confused about sa... ???old idea that ... ???langlands reciprocity program was in part somewhat of a retreat in some sense from original "non-abelian class field theory" program .... ???os??? ..... asf os... ???.... ... ???sa... lossiness from number field to galois rep, ct from galois rep to l-fn ... ???os??? ... asf os... ???.....

??w_a_ sa old bit about "how to name number fields" os.... ????in connection with sa... ???contentfulness of "galois correspondence" ... ??os??? .... asf os... ???sa... ???bunch of vaguely similar issues .... ???os??? ... ???sa subgps ct gp el;ts ... ???os??? .... asf os... ???sa the picture .... ???... os.... asf os... ???...... ???Sa "artin reciprocity" ... ???sa line bundles .... os... asf os... ???......

??what's the relationship between baez's "zeta structure type of a z-set" and ... ???sa.... "structure of being a separable f_p-alg ew point of scheme x over it" ???? os??? ..... asf os....
???how much have we been through this before??? os??? ... ???wa sa non-invertible morphisms between "z-sets over y" ?? .... os... asf os... ???.....

??so w_a_ strategy "figure out what ag th it is that the things that have zeta fns (namely, ... ???....) are comm monoids in the smfcca of coherent sheaves over, and then develop concept of l-function of just plain coherent sheaf over it" ??? .... ???os???? .... ????maybe something strange here??? os???.....