<SEC-DOCUMENT>0001675149-17-000025.txt : 20170407
<SEC-HEADER>0001675149-17-000025.hdr.sgml : 20170407
<ACCEPTANCE-DATETIME>20170407162327
ACCESSION NUMBER:		0001675149-17-000025
CONFORMED SUBMISSION TYPE:	4
PUBLIC DOCUMENT COUNT:		1
CONFORMED PERIOD OF REPORT:	20170405
FILED AS OF DATE:		20170407
DATE AS OF CHANGE:		20170407

ISSUER:		

	COMPANY DATA:	
		COMPANY CONFORMED NAME:			Alcoa Corp
		CENTRAL INDEX KEY:			0001675149
		STANDARD INDUSTRIAL CLASSIFICATION:	ROLLING DRAWING & EXTRUDING OF NONFERROUS METALS [3350]
		IRS NUMBER:				811789115
		STATE OF INCORPORATION:			DE
		FISCAL YEAR END:			1231

	BUSINESS ADDRESS:	
		STREET 1:		390 PARK AVENUE
		CITY:			NEW YORK
		STATE:			NY
		ZIP:			10022-4608
		BUSINESS PHONE:		212-518-5400

	MAIL ADDRESS:	
		STREET 1:		390 PARK AVENUE
		CITY:			NEW YORK
		STATE:			NY
		ZIP:			10022-4608

	FORMER COMPANY:	
		FORMER CONFORMED NAME:	Alcoa Upstream Corp
		DATE OF NAME CHANGE:	20160520

REPORTING-OWNER:	

	OWNER DATA:	
		COMPANY CONFORMED NAME:			FLYNN TIMOTHY PATRICK
		CENTRAL INDEX KEY:			0001550322

	FILING VALUES:
		FORM TYPE:		4
		SEC ACT:		1934 Act
		SEC FILE NUMBER:	001-37816
		FILM NUMBER:		17750020

	MAIL ADDRESS:	
		STREET 1:		JPMORGAN CHASE & CO.
		STREET 2:		270 PARK AVENUE
		CITY:			NEW YORK
		STATE:			NY
		ZIP:			10017
</SEC-HEADER>
<DOCUMENT>
<TYPE>4
<SEQUENCE>1
<FILENAME>edgar.xml
<DESCRIPTION>PRIMARY DOCUMENT
<TEXT>
<XML>
<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2017-04-05</periodOfReport>

    <issuer>
        <issuerCik>0001675149</issuerCik>
        <issuerName>Alcoa Corp</issuerName>
        <issuerTradingSymbol>AA</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001550322</rptOwnerCik>
            <rptOwnerName>FLYNN TIMOTHY PATRICK</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>390 PARK AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK,</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10022-4608</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2017-04-05</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>967</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>33.85</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>3045</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value></value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes></footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Marissa Earnest (Assistant Secretary), by power of attorney</signatureName>
        <signatureDate>2017-04-07</signatureDate>
    </ownerSignature>
</ownershipDocument>
</XML>
</TEXT>
</DOCUMENT>
</SEC-DOCUMENT>
