Re:I no longer understand my PhD dissertation
by wbl on Monday February 15, 2016 @01:27AM
(#11101814)
That doesn't help. Arthur has written a very nice hundred page introduction to the trace formula. You can read that, and it won't tell you why you should care about the trace formula. But if you know Langlands-Tunnels and how it was proven, or how Jacquet-Langlands was proven, you already know to care about the trace formula because you know that it will prove similar results.
The abstraction is necessary: you cannot do algebraic geometry with varieties alone. But while the core of the subject is a multithousand page jewel of abstraction, Vakil is a perfectly readable, example filled introduction to algebraic geometry, covering most of the contents of the glory that is EGA.
Only the rare lemmas are intrinsically interesting. Most often it's the theorems that are worth knowing as steps on the path to understanding something much more. Those lemmas that get used again and again are named, often descriptively.
The abstraction is necessary: you cannot do algebraic geometry with varieties alone. But while the core of the subject is a multithousand page jewel of abstraction, Vakil is a perfectly readable, example filled introduction to algebraic geometry, covering most of the contents of the glory that is EGA.
Only the rare lemmas are intrinsically interesting. Most often it's the theorems that are worth knowing as steps on the path to understanding something much more. Those lemmas that get used again and again are named, often descriptively.