Math 203C (Algebraic Geometry), UCSD, spring 2013
Problem Set 5 (due Friday, May 17)
Solve the following problems, and turn in the solutions to four of them. Throughout this
problem set, let k be an a
Quiz #2
CHEM 6A
Name
Student ID
Discussion
Section
Person on Right
Person on Left
DO NOT BEGIN EXAM UNTIL INSTRUCTED TO DO SO
PLEASE READ THE FOLLOWING BEFORE BEGINNING THE QUIZ
A periodic table and e
Math 203C (Algebraic Geometry), UCSD, spring 2013
Solutions for problem set 1
1. (a) Suppose that f is ane. For x X , we may determine f 1 (x) by pulling back
along the canonical map Spec (x) X . We m
Math 203C (Algebraic Geometry), UCSD, spring 2013
Problem Set 3 (due Wednesday, May 1)
Solve the following problems, and turn in the solutions to four of them. Note: no classes
April 2226 because Ill
Math 203C (Algebraic Geometry), UCSD, spring 2013
Solutions for problem set 3
1. (a) Let K be the kernel of f . By hypothesis, there is another surjection f : F M
with F a nite free R-module such that
Math 203C (Algebraic Geometry), UCSD, spring 2013
Problem Set 2 (due Wednesday, April 17)
Solve the following problems, and turn in the solutions to four of them.
1. (a) It was shown in class that if
Math 203C (Algebraic Geometry), UCSD, spring 2013
Problem Set 1 (due Wednesday, April 10)
Solve the following problems, and turn in the solutions to four of them. As usual, please
document any collabo
Math 203C (Algebraic Geometry), UCSD, spring 2013
Solutions for problem set 2
1. (a) We rst check that S/R is free on the generator dx. On one hand, it is clear that
dx generates S/R since S is a quot
Math 203C (Algebraic Geometry), UCSD, spring 2013
Solutions for problem set 4
1. Suppose that R is perfect and noetherian. For I an ideal of R, put I 1/p = cfw_x1/p : x I ;
this is again an ideal of R
Math 203C (Algebraic Geometry), UCSD, spring 2013
Problem Set 4 (due Wednesday, May 8)
Solve the following problems, and turn in the solutions to four of them. (Note that there
is a second page!)
1. I
Math 203C (Algebraic Geometry), UCSD, spring 2013
Solutions for problem set 7
1. The map GL(m) Spec Z ZJ VJ is the multiplication map on functors of points. The
map VJ GL(m) Spec Z ZJ is dened on func
Math 203C (Algebraic Geometry), UCSD, spring 2013
Problem Set 7 (due Wednesday, June 5)
Solve the following problems, and turn in the solutions to four of them, including at most
two of 13 and at most
Math 203C (Algebraic Geometry), UCSD, spring 2013
Problem Set 6 (due Wednesday, May 29)
Solve the following problems, and turn in the solutions to four of them. No homework
due Wednesday, May 22 due t
Math 203C (Algebraic Geometry), UCSD, spring 2013
Solutions for problem set 6
1. We may assume that U = Spec(A) is ane. Since f is ane, U = f 1 (U ) is also
ane; write it as Spec(B ). Choose elements
Math 203C (Algebraic Geometry), UCSD, spring 2013
Solutions for problem set 5
1. (a) We have X/k = P3 /k O(4) = O because the canonical sheaf on Pn is O(n 1).
k
k
To compute H 1 (X, OX ), we may write
CHEM 6A ZIMMERMANN
REVIEW SESSION 2
PAGE 1
CHAPTER 4
Ionization Energy and Shell Structure
nth ionization energy, In: X(n-1)+ Xn+ + e
I1 increases with group number within a period and decreases wit