In Tsarist Russia a man was tried for murdering a fellow student. The
fellow student had discovered that the man, who had claimed membership
in a great international revolutionary movement and was supposedly off
attending one of these international meetings, was actually living in
a cave (probably Moscow or St. Petersburg) writing and producing his
own literature. The man about to be exposed as a fraud killed the
student. He was tried in a tsarist court and sentenced to prison.
While in prison he wrote an early revolutionary manifesto. What is the
man's name?

Hello.

I believe that you're thinking of Sergei Nechaev (1847-1883).  

In 1869, Nechaev, who claimed membership in an organization called the
"World Revolutionary Alliance" (or sometimes the "Secret Revolutionary
Committee"), was attempting to organize a group of student radicals in
Moscow.  When a fellow student named Ivanov came to believe that
Nachaev was a fraud, Nechaev murdered him.  Nechaev became famous for
his revolutionary manifesto "Catechism of a Revolutionary."  He was
also the basis for Fyodor Dostoevsky's novel "Devils."

Source:

"In 1869, while still abroad, Dostoevsky learned the details of the
notorious Nechaev case from his reading of Russian newspapers. A young
student named Ivanov, a member of a secret revolutionary committee or
cell called a 'group of five', had been murdered by Sergei Nechaev...
Why was Ivanov murdered?  Most likely because he had begun to suspect
Nechaev was nothing more than an impostor and a con-man, and was
threatening to expose them all to the authorities."

source: Introduction, page ix
Devils (Oxford World's Classics)
by Fyodor M. Dostoevsky, Michael R. Katz (Editor), read using "search
inside" on Amazon.com
http://www.amazon.com/exec/obidos/tg/detail/-/0192838296/


Also see:

'On a visit to Switzerland, Nechaev conned Bakunin into believing that
he was the head of a revolutionary organization with hundreds of
members. To impress Nechaev, Bakunin boasted of leading the World
Revolutionary Alliance, which despite Bakunin's intimations had at the
time exactly two members--Bakunin and Nechaev.
 Nechaev returned to Russia as an agent of this "organization" with
instructions to form a Moscow branch. There he encountered a student
named Ivanov who expressed doubts about Nechaev's credentials. To
exact the total obedience he expected of the other members he had
recruited, Nechaev induced them to collaborate in Ivanov's murder,
falsely claiming he was a police spy. The deed was done in November
1869, and the body was dumped into an ice-covered pond, the whole
episode forming the basis for Dostoevsky's antirevolutionary novel,
Devils. All of the perpetrators were caught but Nechaev, who escaped
back to Switzerland. In 1872, he was arrested there and deported back
to Russia, where ten years later he died of scurvy in prison.
In tandem with Bakunin, Nechaev has left a mark on history through the
fruit of their collaboration, the "Catechism of a Revolutionary."'
source:
ORGANIZING REVOLUTION: THE RUSSIAN TERRORISTS, hosted by princeton.edu
http://pup.princeton.edu/chapters/s7346.html

'Upon his return to Russia Nechaev formed the secret, cell based
organization, People?s Vengeance. One student member of the
organization Ivan Ivanovich Ivanov questioned the very existence of
the Secret Revolutionary Committee that Nechaev claimed to be the
representative of. This honest appraisal of Nechaev?s modus operanti
required action. "On the evening of 21 November 1869 the victim was
accordingly lured to the premises of the Moscow School of Agriculture,
a hotbed of revolutionary sentiment, where Nechayev did him to death
by shooting and strangulation, assisted without great enthusiasm by
three dupes...'
source: Nihilism
http://www.angrynerds.com/nihilism.pdf

---------
search statregy:
"murder of a student" russian radicals
nechaev, ivanov
amazon.com nechaev, ivanov

I hope Nechaev is the individual whom you had in mind.  If not, please
let me know via the "request clarification" feature. Thanks.