Basement floor is serated ( not one flat surface) Have had heavy rains in the area that i live and now I am seeing stains on the carpet in the basement. Do not have padding, Just carpet laying on the basement floor. Where there are cracks in the floor, there are stains on the carpet. What caused this and how do i fix it.

I don't understand how a basement floor can be serrated, but I'm guessing that the stains in the carpet could possibly be mold. Without a description of their color, and odor, if any, it's hard to say much more. I think someone has to look at it and test it.

The carpet laying on the basement floor is tan, there are dark tan lines where the floor is sereated (There are cut lines in the concrete for expansion, I call them serated) There is no odor, and can feel no dampness.

A few things can cause this to happen.
one is mold developing because of elevated moisture levels where the expansion joint is located. I know you feel its dry but it does not take much to harbor mold.
Another reason for the stains is that there is air flow in that area where the joints are located. The carpet acts like a filter. As the air moves through the space the carpet holds the fine dust particals thus the stain lines.

The only way to repair this is to remove the carpet and seal the cracks with a silicon caulk to seal the openeings. Then use a good quality sub-floor padding then lay new carpet down. You could try cleaning it but I do not think you will have any luck. You may find the underside of the carpet is turning black. If that is the case, you need to address the dampness under the floor first. As this is a sign of water.

Are there metal strips in the expansion joints? The tan color sounds like rust. Home Care Club's silicon fix sounds like a worthwhile idea. Make sure the areas are clean and dry before trying it.