What is the resolution of the conflicts in "The Legend of Sleepy Hollow"?

Ironically,
the resolution of the conflicts involves that which Ichabod initiates himself; namely, the
interest in the supernatural.  And, it is with his character Ichabod Crane that Irving pokes fun
of supernatural conventions and parodies the Romantic hero.

Although Ichabod,
a native of Conneticut and the schoolmaster, becomes an authority of Cotton Mather's
History of New England Witchcraft;  he utilizes this "appetite for the
marvellous" as a means to appeasing his physical appetite by ingratiating himself with the
old Dutch wives, listening to their tales of ghosts and goblins after they have fed him. But, on
his walks home, Ichabod is fearful with the "terrors of the night, phantoms of the mind
that walk in darkness."

His interest in Katrina Van Tassel, the only
child of a wealthy Dutch farmer, leads Ichabod to the Van Tassel farm where his fancy with food
and plenty is captured. Thus, he essays to gain the affections of Miss Van Tassel.  However,
there is a rival for Katrina's love:  Brom van Brunt, "the hero of the county
round."  So, Ichabod disguises his advances upon Katrina by making visits as the
singing-master, and he is very wary of his adversary, Brom, not affording him opportunities for
combat. Nevertheless, Brom is able to stop up the chimney in the schoolhouse, and he and his
friends turn things topsy-turvy.

When Ichabod Crane is invited to a party at
the Van Tassels' he arrives on a horse that is theof Brom Bones's steed Daredevil.  At the
party, more ghost stories are recounted; Brom claims to have defeated the Hussian in a race.
This story and all the others that Ichabod has heard resound in his memory as he sets out for
home.  Suddenly, Ichabod perceives the shadowy form of a horseman in the middle of the road; so,
he urges his horse to run, but the other stays in step with him.  When the rider passes before
the moon, Ichabod sees that he is headless, and that he carries his head upon the pommel of his
saddle. As he attempts to flee on the back of old Gunpowder, the horse manages to cross the
bridge, so Ichabod looks back. It is then that Ichabod realizes that the pursuing headless
horseman is about to hurl his carried head.  Ichabod hurries, but is tumbled headlong into the
dust.

The next morning the schoolmaster does not appear, nor is he ever seen
again. A search party is formed, but only a large pumpkin and small bundle of Crane's is found.
Tales of Ichabod Crane burgeon, tales that the headless horseman carried off Crane and the
schoolhouse

was reported to be haunted by the ghost of the
unfortunate pedagogue.... 

While Brom Bones laughs and
gives a "knowing look" whenever the old country wives  mention Ichabod Crane, they,
nevertheless, insist that Ichabod has been "spirited away by spiritual
means."

Thus, the conflict between Brom Bones and Ichabod Crane is
resolved by this disappearance of Crane.  In an ironic twist of fate, Crane becomes the object
of his own interests:  He himself becomes a part of supernatural tales.