DVR and Irreducible Plane Curves

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Covers the topology of Adeles and their relationship with quadratic forms, polynomial varieties, and finiteness properties.

Covers cohomology in real projective spaces, focusing on associative properties and algebraic structures.

Explores algebraic structures, classes of examples, and properties of cyclic groups.

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

Explores Dedekind rings, integral extensions, and noetherian rings in algebraic structures.

Explores irreducible polynomials, focusing on their degree and roots in different fields.

Covers the normalization process of plane algebraic curves, focusing on irreducible polynomials and affine curves.

Explores integration on H_pxH and arithmetic properties, including norms, structures, and polynomial factorization.

Covers the study of projective varieties and their relation to compact manifolds.

Covers proper actions of groups on Riemann surfaces and introduces algebraic curves via square roots.