@Bo Goebel , yes that's how it works. Each year after your syndicator's CPA completes the tax return for the property, he will issue you an IRS Form 1065 Schedule K1 which will include your capital contributed in equity (your investments amount) and your net profit/loss based on all property tax deductions. This would be used for filing your taxes. The profit/loss is your prorated share of the total property profit/loss after deductions that is reported to the IRS by the property GP and would be used for your own tax return.
Normally, a loss is reported due to depreciation and expenses in the first few years, in which case you would owe no taxes on any cash return you earned for that year from the property.
Your tax adviser/CPA can give you better details for your unique tax situation (note that I'm not a CPA).
@Mitch Provost is right. You will receive a K-1 from the partnership. The only stipulation I will add is that this one K-1 only makes up one piece of the puzzle. Your overall deduction may be limited to the extent you have other passive (other syndication income) income.
Also, in the event you have income from this partnership interest, you are liable for taxes regardless if you received any cash. However, most partnership agreements state that cash will be distributed to cover any income tax due.
As always talk with your CPA regarding your unique situation.
@Bo Goebel I second what @Mitch Provost and @Account Closed said about the taxation of your K-1. Essentially as an equity partner in a syndication, you're benefiting as a partial property owner. This is one of the main differentiation's of syndications from REITs.
Also, I know you used the amount as an example, but wanted to clarify, $10,000 will not be enough to invest in majority of syndications unless you're doing it through crowdfunding platform.