Scheme theory is a branch of algebraic geometry that explores the properties of schemes, which are the fundamental objects of study in this field. Developed in the 1960s by mathematicians such as Alexander Grothendieck, scheme theory provides a unifying framework for various concepts in geometry and algebra. A **scheme** is locally defined by the spectra of rings, specifically the spectrum of a commutative ring, which can be thought of as a space of prime ideals.

Tropical geometry is a relatively new area of mathematics that arises from 'tropicalizing' classical algebraic geometry. In classical algebraic geometry, one studies varieties defined over fields, typically using tools from linear algebra, polynomial equations, and algebraic structures. Tropical geometry, on the other hand, replaces the usual operations of addition and multiplication with tropical operations.

The term "China doll" can refer to a couple of different things, depending on the context: 1. **Porcelain Doll**: A "China doll" is often a type of doll made from porcelain or china, characterized by its delicate features, painted facial expressions, and sometimes intricate clothing. These dolls have been popular collectibles, especially in the 19th and early 20th centuries. They are known for their fragile nature and often depict various historical or cultural themes.

Reductionism is a philosophical and scientific approach that seeks to understand complex systems by breaking them down into their simpler, more fundamental components. The idea is that by studying the individual parts, one can gain insights into the behavior and properties of the whole system. Reductionism can be applied in various fields, including: 1. **Philosophy of Science:** In this context, reductionism often involves explaining higher-level phenomena in terms of lower-level scientific theories.