Homework assignments

Homework 1, due Sep. 17.
Problem on p. 9 in [Mumford],
[Hartshorne]
Ch. 1 Ex. 1.3, 1.1(b), 1.4,
Ch. 2 Ex. 1.1.

Homework 2, due Oct. 1.
Verify that Definition 4 on page 20 in [Mumford] does define a sheaf,
Problem on p. 32 in [Mumford],
Problem on p. 40 in [Mumford],
Problem on p. 39 in [Mumford],
[Hartshorne]
Ch. 1 Ex. 3.1, 3.17 (c, d, e).

Homework 3, due Oct. 15.
[Hartshorne]
Ch. 1 Ex. 1.11, 1.12,
Ch. 1 Ex. 2.16, 2.17 (b,c),
Verify Porposition 5 on page 46 in [Mumford],
[Hartshorne]
Ch. 1 Ex. 4.1, 4.3. 4.4, 4.5, 4.6.

Homework 4, due Oct. 29.
[Hartshorne]
Ch. 2 Ex. 2.13, 2.19,
2.3, 2.7, 2.8,
3.9, 3.2.

Homework 5, due Nov. 12 (more to come).
Problem on p. 111 in [Mumford],
Problem on p. 120 in [Mumford],
Find a sheaf map over a topological space consisting of 3 points such that it is surjective on all stalks but not surjective over all open sets,
[Hartshorne]
Ch. 2 Ex. 4.2, 4.3,