<PAGE>

                                                                   EXHIBIT 10.35

                           Indemnification Agreement

                         Dated as of January 10, 2001

     WHEREAS, Exodus Communications, Inc. ("Exodus"), Einstein Acquisition Corp.
("Acquisition Corp."), Global Crossing GlobalCenter Holdings, Inc., GlobalCenter
Holding Co. ("Holdings"), GlobalCenter Inc ("Company") (Exodus, Holdings and the
Company, collectively, the "Indemnitees"), and Global Crossing North America,
Inc. ("Global Crossing NA") have entered into an Agreement and Plan of Merger
(the "Merger Agreement") dated as of September 28, 2000, which provides for the
merger (the "Merger") of Acquisition Corp. with and into Holdings;

     WHEREAS, the Board of Directors of Company has adopted the GlobalCenter
Inc. Management Stock Plan effective as of January 7, 2000, (the "Plan");

     WHEREAS, the individuals who are signatories hereto (each a "Participant")
and the Company have entered into Non-Statutory Stock Option Agreements under
the GlobalCenter Inc. Management Stock Plan prior to the Closing Date (as
defined in the Merger Agreement) of the Merger (the "Stock Option Agreements");

     WHEREAS, the Stock Option Agreements (and in the case of Leo J. Hindery,
Jr., also an employment agreement ("Hindery Employment Agreement")) provide
that, in the event that any amounts the Participant receives or is deemed to
receive in connection with the options issued under the Plans or pursuant to the
Hindery Employment Agreement, result in the imposition of excise tax under
Section 4999 of the Internal Revenue Code of 1986, as amended (the "Code") (or
any successor provision or comparable federal, state, or local excise tax
provision), the Company will make the Participant whole with a payment for the
entire amount of such excise tax (including any excise tax on such payment), as
well as any attendant employment taxes and/or income taxes and any penalties
and/or interest assessed in connection with any of the foregoing (the "Tax
Restoration Payment").

     NOW, THEREFORE, in exchange for the receipt of consideration, the adequacy
of which the parties hereby acknowledge, and intending to be legally bound
hereby, the parties agree as follows:

     1.  Subject to the provisions of this Agreement, Global Crossing NA hereby
agrees to pay to, or on behalf of, each Participant any Tax Restoration Payment
and agrees to make such payment upon the due date of the excise tax or any
attendant income tax, employment tax, penalty or interest to which the Tax
Restoration Payment relates; provided, however, that the failure of Global
Crossing NA to timely pay the Tax Restoration Payment to the Participant shall
not relieve Global Crossing NA of its obligations for such payment under the
terms of this Agreement.  Global Crossing NA shall remit to the Internal Revenue
Service (the "IRS") or any other taxing authority such payments as are required
by applicable withholding or similar laws.

     2.  Each Participant agrees to look solely to Global Crossing NA (or its
successors in interest) for any Tax Restoration Payment and expressly releases
and waives any and all claims
<PAGE>

with respect to the Tax Restoration Payment or the taxes which are the subject
of the Tax Restoration Payment against the Company and its owners (with the
exception of Global Crossing NA), agents, officers, shareholders (with the
exception of Global Crossing NA), employees, directors, attorneys, subscribers,
subsidiaries, affiliates and successors or assigns, including Exodus,
Acquisition Corp., Holdings and their owners, agents, officers, shareholders,
employees, directors, attorneys, subscribers' subsidiaries, affiliates,
successors and assigns (the "Releasees"). By signing below, each Participant
expressly waives any benefits of Section 1542 of the Civil Code of the State of
California, which provides as follows:

            "A GENERAL RELEASE DOES NOT EXTEND TO CLAIMS
            WHICH THE CREDITOR DOES NOT KNOW OR SUSPECT TO
            EXIST IN HIS FAVOR AT THE TIME OF EXECUTING THIS
            RELEASE, WHICH IF KNOWN BY HIM, MUST HAVE
            MATERIALLY AFFECTED HIS SETTLEMENT WITH THE
            DEBTOR."

     3.  Each Participant and the Indemnitees hereby agrees to take the position
that any payment and/or benefit received by the Participant in connection with
the Merger is not an "excess parachute payment" within the meaning of Section
4999(b) and 280G(b) of the Code (or any successor provision or comparable
federal, state, or local excise tax provision) and thus does not give rise to
any excise tax under Section 4999(a) of the Code (or any successor provision or
comparable federal, state, or local excise tax provision).

     4.  (a)  The Participant, the Indemnitees, and Global Crossing NA hereby
agree that, the Participant  (or, if so notified by the IRS or a Participant, an
Indemnitee) will notify Global Crossing NA in writing of any claim by the IRS
(or in the case of a noticed Indemnitee, by the Participant, that, if
successful, would require the payment by Global Crossing NA of any Tax
Restoration Payment  or any other payment hereunder.  Such notification shall be
given as soon as practicable but no later than ten business days after the
Participant or an Indemnitee, as applicable, is informed in writing of such
claim and shall apprise Global Crossing NA of the nature of such claim and the
date on which such claim is requested to be paid.  Neither the Participant nor
any Indemnitee shall pay such claim prior to the expiration of the thirty-day
period following the date on which it gives such notice to Global Crossing NA
(or such shorter period ending on the date that any payment of taxes with
respect to such claim is due).

     (b) If Global Crossing NA notifies the Participant or, if applicable, an
Indemnitee, in writing prior to the expiration of such period that it desires to
contest such claim, the Participant and any Indemnitee shall (i) give Global
Crossing NA any information reasonably requested by Global Crossing NA relating
to such claim, (ii) take such action in connection with contesting such claim as
Global Crossing NA shall reasonably request in writing from time to time,
including, without limitation, accepting legal representation with respect to
such claim by an attorney reasonably selected by Global Crossing NA, (iii)
cooperate with Global Crossing NA in good faith in order to effectively contest
such claim, and (iv) permit Global Crossing NA to participate in any proceedings
relating to such claim; provided, however, that Global Crossing NA shall bear
                        --------  -------
and pay directly all costs and expenses (including additional interest and
penalties) incurred in connection with such contest and shall, whether or not
Global Crossing NA provides notification pursuant to this Section 4(b),(i)
indemnify and hold the Participant harmless, on an


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<PAGE>

after tax basis, for any excise tax imposed as a result of such representation
and payment of costs and expenses and (ii) indemnify any Indemnitee for any Tax
Restoration Payment paid by such Indemnitee and for any tax, penalty or interest
associated with a failure to meet any withholding or reporting obligation of the
IRS or any other taxing authority.

     (c) Without limiting the foregoing, Global Crossing NA shall control all
proceedings taken in connection with such contest and, at its sole option, may
pursue or forego any and all administrative appeals, proceedings, hearings and
conferences with the taxing authority in respect of such claim and may, at its
sole option, either direct the Participant to pay the tax claimed and sue for a
refund or contest the claim in any permissible manner, and the Participant and
any affected Indemnitee agree to prosecute such contest to a determination
before any administrative tribunal, in a court of initial jurisdiction and in
one or more appellate courts, as Global Crossing NA shall determine; provided,
                                                                     --------
however, that if Global Crossing NA directs the Participant to pay such claim
-------
and sue for a refund, Global Crossing NA shall advance the amount of such
payment to the Participant, on an interest-free basis, and shall indemnify and
hold the Participant harmless, on an after-tax basis, from and excise tax
imposed with respect to such advance or with respect to any imputed income with
respect to such advance; provided, further, that if the Participant is required
                         --------  -------
to extend the statute of limitations to enable Global Crossing NA to contest
such claim, the Participant may limit this extension solely to such contested
amount.

     (d) If, after the receipt by the Participant of any amount paid or advanced
by Global Crossing NA pursuant to this letter, the Stock Option Agreement, or
the Hindery Employment Agreement, the Participant becomes entitled to receive
any refund with respect to a Tax Restoration Payment, the Participant shall
promptly pay to Global Crossing NA the amount of such refund received (together
with any interest paid or credited thereon after taxes applicable thereto).  If,
after the receipt by the Participant of an amount advanced by Global Crossing NA
pursuant to this letter, the Stock Option Agreement, or the Hindery Employment
Agreement, a determination is made that the Participant shall not be entitled to
any refund with respect to such claim and Global Crossing NA does not notify the
Participant in writing of its intent to contest such denial of refund prior to
the expiration of thirty days after such determination, then such advance shall
be forgiven and shall not be required to be repaid and the amount of such
advance shall offset, to the extent thereof, the amount of the Tax Restoration
Payment required to be paid.

     5.  The Agreement is made under and construed pursuant to the laws of the
State of California.

     6.  This Agreement shall be binding on the successors and assigns of Global
Crossing NA, the Indemnitees, and any Participant.

     7.  This Agreement may be executed in one or more counterparts, each of
which when so signed shall be deemed to be an original, and such counterparts
together shall constitute one and the same instrument.  In lieu of the original,
a facsimile transmission or copy of the original shall be as effective and
enforceable as the original.


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<PAGE>

     IN WITNESS WHEREOF, the parties hereto have caused this Agreement to be
executed as of the date first written above.


EXODUS COMMUNICATIONS, INC.                     EINSTEIN ACQUISITION CORP.


By: /s/ R. Marshall Case                        By: /s/ Adam W. Wegner
   ---------------------------------               ----------------------------

Name R. Marshall Case                           Name: Adam W. Wegner
    --------------------------------                 --------------------------

Title: Executive Vice President,                Title: President, Chief
       Finance and Chief Financial                     Financial Officer and
       Officer                                         Secretary
      ------------------------------                  -------------------------

GLOBAL CROSSING NORTH AMERICA, INC.             GLOBALCENTER INC.


By: /s/ Joseph P. Clayton                       By: /s/ Leo J. Hindery, Jr.
   ---------------------------------               ----------------------------

Name:  Joseph P. Clayton                        Name: Leo J. Hindery, Jr.
     -------------------------------                 --------------------------

Title: Chief Executive Officer                  Title: Chief Executive Officer
      ------------------------------                  -------------------------

GLOBALCENTER HOLDING CO.

By: /s/ Leo J. Hindery, Jr.
   ---------------------------------

Name: Leo J. Hindery, Jr.
     -------------------------------

Title: Chief Executive Officer
      ------------------------------

PARTICIPANTS:

/s/ Leo J. Hindery, Jr.                         /s/ Peter Baron
------------------------------------            -------------------------------
Leo J. Hindery, Jr.                             Peter Baron

/s/ Derek Chang                                 /s/ Mark J. Coleman
------------------------------------            -------------------------------
Derek Chang                                     Mark J. Coleman


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<PAGE>

/s/ Grace De Latour                             /s/ Eric Kirsten
---------------------------                     ---------------------------
Grace De Latour                                 Eric Kirsten


/s/ David L. Klott                              /s/ David Krone
---------------------------                     ---------------------------
David L. Klott                                  David Krone


/s/ Lisa Perreault                              /s/ Laurie Priddy
---------------------------                     ---------------------------
Lisa Perreault                                  Laurie Priddy


/s/ Bruce Stewart                               /s/ Barbara Wood
---------------------------                     ---------------------------
Bruce Stewart                                   Barbara Wood


/s/ Gregory Liberman                            /s/ Bryan Gaynor
---------------------------                     ---------------------------
Gregory Liberman                                Bryan Gaynor


/s/ Carolyn Sharks                              /s/ Lee Munsell
---------------------------                     ---------------------------
Carolyn Sharks                                  Lee Munsell


/s/ Craig Fischer
---------------------------                     ---------------------------
Craig Fischer




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