Magicka Arcanist PvP Build
Magicka Arcanist PvP builds are incredibly capable in terms of survivability, and can keep the pressure up against opponents exceptionally well with powerful sustained damage over time. Their main selling point is access to incredibly strong combo attacks that leave enemies helpless as you drain their health away.
Gear Sets
Soulshine: I waited for a long time to be able to use this effectively, and Arcanists really... "shine" with this set. When you use Pragmatic Fatecarver, you will increase your weapon and spell damage by a hefty margin - nice, simple and powerful. You can get this set from Reaper's March.
Rallying Cry: A nice combo set that adds a batch of damage and a batch of critical resistance when you critically heal, which is easy to do in PvP. You can get this from gear mechants in Cyrodiil.
Sea-Serpent's Coil/Markyn Ring of Majesty: The Sea-Serpent's Coil is the best all-round for increasing your damage output by a massive margin, which when combined with Rallying Cry and Soulshine will make your main attack absolutely shred opponents. If the snare is too much, try Markyn Ring of Majesty which is still nicely balanced.
Roska the Warped: You're going to need to keep on top of your resources if you're going all-out offensive here, and this is how you do that. You can get this from Scrivener's Hall, and it adds a ton of both Magicka and Stamina recovery, escalating over the duration of a fight.
Armor of the Trainee: A nice extra one-piece bonus that gives a big boost to health. You can get this easily and cheaply by checking out guild traders.
Skills
Rune of the Colorless Pool: Allows you to stun the opponent after a brief delay, which is perfect for setting them up for your ultimate. Applies Minor Brittle, increasing critical damage taken.
Writhing Runeblades: A useful ranged spammable that is primarily designed to easily generate Crux, which will empower your Pragmatic Fatecarver.
Cephaliarc's Flail: Another tool for generating Crux which also serves as a 5% damage taken debuff and an execute.
Camouflaged Hunter: Use this to provide Major Prophecy, boosting your critical chance significantly.
Pragmatic Fatecarver: This is your main damaging ability, dealing a ton of damage over its duration, moreso if you have three Crux active. Also gain a shield while casting.
The Tide King's Gaze: Your primary ultimate, only to be used when the enemy is stunned in place with Rune of the Colorless Pool.
Resolving Vigor: A great source of passive healing that also provides Minor Resolve, boosting your damage resistance.
Impervious Runeward: A very potent shield that acts kind of like a parry, becoming very strongly empowered in the first second of its use. Use this when you see powerful hits coming your way.
Cruxweaver Armor: Your main source of Major Resolve, which also generates Crux when taking damage. Any enemy that hits you is inflicted with Minor Breach, reducing their resistances.
Elemental Drain: Your source of Major Breach, allowing you to reduce the resistances of your target while also gaining Magicka back when attacking them.
Recuperative Treatise: A source of Crux and resources along with applying Major Sorcery to both bars, boosting your damage output.
Sanctum of the Abyssal Sea: An excellent defensive ultimate that will give you a ton of damage mitigation over its duration before returning all of the damage back in the form of an area around you over ten seconds.
Champion Points
Thaumaturge: This class shines best with damage over time abilities, and Thaumaturge will help with buffing that further. For most abilities that you will be using, Thaumaturge and Biting Aura will stack.
Biting Aura: This class in particular really benefits from a buff to area damage, making this a smart choice for increasing your burst damage potential, so make sure you always have it slotted.
Ironclad: Since direct damage is so common, it is important to also defend against it. That is where Ironclad comes in, boosting your mitigation against this damage type.
Resilience: No matter what the meta is running, critical damage will always be a big part of what many players build around in PvP. It is important to defend against that, and Resilience will help you there in combination with Impenetrable armour pieces.
Boundless Vitality: Every bit of health makes a difference, especially in some of the tougher content that The Elder Scrolls Online has to offer. This will help you bump yours up a little more, increasing your survivability.
Slippery: In PvP, pinning your opponent down with CC before you burst them down is important. This will prevent that from happening to you so easily, making it an important addition.
Rejuvenation: Recoveries are important for every role. For healers, it is essential for keeping your group alive, for tanks, it is the source of most of your buffs and debuffs, for DPS, you can't deal damage with no fuel, and in PvP, no resources means death.
Celerity: Extra movement speed is an amazing boost in all content. In PvE, it helps massively with avoiding nasty mechanics, and in PvP, it allows you to run circles around your opponents.
Mundus Stone
The best Mundus Stone to use on this build is the Lover for significantly better Penetration. The Lover gives the best overall boost to damage output on average against players, especially since players in PvP tend to run a lot of resistance. However, if you need more recovery, consider the Atronach instead.
Food Buff
The Clockwork Citrus Filet offers an incredibly useful spread of Max Health, Max Magicka, Health Recovery and Magicka Recovery, making it perfect for Magicka-focused PvP builds. If you can't afford its hefty cost, go with the Witchmother's Potent Brew instead, offering similar stats but no Health Recovery.
Race
My preferred race to run for this build is a Breton for their superior sustain. However, if you feel that you are managing your resources well enough, then you can switch to a High Elf (Altmer) for more overall damage, or Dark Elf (Dunmer) for almost the same damage as the High Elf with a little extra stamina for survivability as well.
Potion
PvP builds generally work best when running Immovability potions, which grants a lengthy immunity to snares, immobilizations and stuns. It's good to carry some potions to reveal invisibility as well to counter Nightblades.
Mortality
Due to the slow-roller nature of Arcanists in PvP, they benefit greatly from both the Undeath passive of Vampirism and the Mist Form skill for mobility. Therefore, if you can manage the sustain, running a Vampire is recommended for this build.
Notes
Magicka Arcanists can survive seemingly endlessly in PvP, having access to some of the best survivability tools in the game. With powerful shields, strong healing and potent buffs and debuffs, the trick with Magicka Arcanist PvP builds is to stall out until the right moment, debuff your opponent, stun them and let loose a massive burst of sustained damage that is incredibly difficult to recover from.