Initially with Peak Oil the more likely scenario is to have higher inflation. Thus increasing the market price of your house but the total debt value stays constant. That actually increases the equity in your home.
You could be right but I'm not sure. Historically the price of houses is set by the amount people are able and willing to pay for it. That depends on the following factors.
1) Disposable income
2) Interest rates
3) Mortgage requirements
4) Availability
If we look at these factors individually
1) Disposable income
I think we can be fairly certain that PO is going to increase the cost of daily living. That means that the amount of money that you can spare to pay a mortgage will decrease.
I've done some calculations on this. If your monthly expenses increase by $100 per month, it will cut $30.000 of the size of the mortgage you'll be able to afford.
2) Interest rates
Many people believe that the interest rates are going to rise. I'm not so certain of that but if they will it will also have a strong effect on the height of the mortgage you're able to service.
For a typical mortgage a one percent interest rate hike will cut about $25.000 on the amount of mortgage you're able to afford.
3) Mortgage requirements
In the past you could only finance 90% of your house by a mortgage. 10% had to be financed by own means. Now financing goes up to 125%. When confronted with a lot of defaulting, banks may drop that leniency. They probably won't go back to 90%, but even 100% would mean that young adults will have to safe for a few years to get the necessary money to get a house. this will temporarily slow down demand.
4) Availability
Right now the housing market is still very tight. In the next few years I expect this situation to change.
The baby boomer's are now retiring. Within a few years they will start moving to smaller apartments and homes for the elderly which will free up a large part of the housing market. The second generation of baby boomer's has just moved to a house. Therefore the demand will temporarily slow down. This is essentially also what happened in the seventies, which marked the gap between the first and the second generation of baby boomer's.
Secondly a deteriorating economic climate will cause children to stay longer with their parents, reversing the trend that has been going on for the past decades.
The past decades we had a very favorable climate for houses. Wages grew faster than inflation in consumer goods, mortgages became more affordable, and demographic conditions ensured a high demand. When you look at these factors you can understand why for instance the value of my parents house increased by 1000% in the past 20 years. However many of these things are reversible and perhaps will be reversed in the next few years.
So while inflation (or currency deflation) is expected to drive prices up I also see some strong arguments in favor of a decline. It all depends on how the wages will develop. If wage growth is stronger than the factors above, housing prices will stay level or increase. Otherwise they will decline.