Can women study Talmud?
Yes, women _can_ study Talmud.
Generally, however, Judaism recognizes certain differences in men and women. To ignore these differences is to ignore biology — our brains are physically and chemically different, and our needs are different. When it comes to reasoning, men are more likely to pursue theoretical constructs, while women are more pragmatic. Women want to know the law, while men are willing to argue about the property issues involved when my ox gores your cow. For this reason, teaching Talmud to a class of women is generally frowned upon, although some modern Orthodox schools do this today.
Women most certainly have an obligation to study Torah in order to know what to do, and are encouraged to study the Torah itself, the Prophets, law, and countless other works.