By, Core you mean Player's Handbook only? Technically, in 4e, it is all "core".
Here's a PHB-only Elf Polearm Fighter build. If you get to level 12, you qualify for Heavy Blade Opportunity, which allows you to use an At-Will power with Polearm Gamble... provided you continue to use a Glaive. Elf is rough as it doesn't provide a Strength bonus, restricting the build to a starting 18. PHB-only is much more rough.
====== Created Using Wizards of the Coast D&D Character Builder ======
level 11
Elf, Fighter, Pit Fighter
Fighter Talents: Two-handed Weapon Talent
FINAL ABILITY SCORES
Str 21, Con 15, Dex 15, Int 11, Wis 15, Cha 9.
STARTING ABILITY SCORES
Str 18, Con 13, Dex 12, Int 10, Wis 11, Cha 8.
AC: 25 Fort: 25 Reflex: 20 Will: 20
HP: 100 Surges: 11 Surge Value: 25
TRAINED SKILLS
Heal +12, Endurance +12, Athletics +15, Intimidate +9
UNTRAINED SKILLS
Acrobatics +7, Arcana +5, Bluff +4, Diplomacy +4, Dungeoneering +7, History +5, Insight +7, Nature +9, Perception +9, Religion +5, Stealth +7, Streetwise +4, Thievery +7
FEATS
Level 1: Elven Precision
Level 2: Quick Draw
Level 4: Weapon Focus (Heavy Blade)
Level 6: Student of Battle
Level 8: Toughness
Level 10: Blade Opportunist
Level 11: Polearm Gamble
POWERS
Fighter at-will 1: Cleave
Fighter at-will 1: Reaping Strike
Fighter encounter 1: Passing Attack
Fighter daily 1: Villain's Menace
Fighter utility 2: Boundless Endurance
Fighter encounter 3: Sweeping Blow
Fighter daily 5: Rain of Steel
Fighter utility 6: Unbreakable
Fighter encounter 7: Come and Get It
Fighter daily 9: Thicket of Blades
Fighter utility 10: Stalwart Guard
ITEMS
Vicious Glaive +3, Adventurer's Kit, Black Iron Scale Armor +2, Amulet of Protection +3
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