I am applying to graduate schools in the United States this year. I have research experience for one year in algebraic geometry. I learned a lot from this experience, mostly by reading papers, books, and doing calculations. I have produced no publication (algebraic geometry is a hard field). However, I have a conflict with my advisor and therefore can not include him as a recommendation letter provider. So can I omit this experience completely from my CV? would it be ethical? or should I mention it and risk the admissions committee drawing the conclusion that my research performance was bad and therefore reject my application immediately as many people here seem to suggest?
I see no reason to omit it. I see no reason to have the supervisor write a letter of recommendation either. They are independent things. You want the best letters you can get and they seem to be from others here. You also want to show that you have some research experience even if it wasn't sufficient to result in publication.
I assume you mean undergraduate research, of course, which is limited in time and scope. The limitations are, well, limiting in what can be done. With more scope you might have gone further, as you would be expected to do with a more open ended program in a doctoral degree.
List it, even list the name of the supervisor if he has some prominence. But have the letters attest to both your background accomplishments and the probability of your future success.
Most places would consider it improper to contact someone that you didn't include in your application materials. But if they do, and you are questioned on it, just be honest about the situation. Conflicts happen. People know that.