All Episodes

CRT and disjoint union

zariski coarse

J in O(X) V(J) induced topology is the sari ski on X

Left exact right derived coho-delta

G-mod ab enough inj and surj

a question on proj obj of an ab cat

Homotopy equi give same cohomology go

homotopic give same cohomology

phi(mu)/mu congru p mod mu

G trivial and G infinite cyclic

from Z[G]-modules to cochain complex

free Z[G]-module P_* give proj résolution

pf gp cohomology of A*

Subgp of free is free

A* coinduced module

H1(G,M) explains Z failing to be projective Z[G]-module?

Modules exact sequence to complex exact sequence to long exact sequences

H^0(G,M) by definition M^G

Gp coho Hi(G,M) using proj resolution of Z, then Hom_Z[G](-,M) does not depend on projects résolu

Proj résolu Pi to X to 0, then apply left exact F(-) to [Pi to 0] not exact

Z[G] comm off G abelian

O(X) K[Ti]/I(X)

K-Alg k-blinear binary map

pf weak implies strong nustellensatz

cor of Strong nustellensatz; two polys same on X if they are equal modulo I(X)

Path algebra

quiver

Monoid to k-Alf

Finite fi with no common zero generate whole ring

Another pf of weak nustellensatz

Strong and weak nustellensatz

I(X) is radical any subset X in affine space

Any Alf set X in A^n is the zero loci of finite poly

noetherian ring Gilbert basis

Q10 finite height con for exten of wach

chi(g) in 1+ pZp

Q10 g(mu)?

Q9 Fil^0N

（g-1）Fil^kN in my Fil^k-1

N/muN and Dcri

Nygar fil; decreasing; eff off Fil0=N

Cat equi wach and crystalline Zp and Qp

Def of Wach A_F^+; B_F^+

Cor 5.26 ire alg var Dim V(f) d’IMAX-1

Prop5.23 f g integral over k dim good

Prop 5.19 integral alg var dim X = dim U

Thm5.15 dimA/f

Cor 5.14 dim m / m2

Thm5.12 Krull principal ideal thm

Lemma5.11 dimA=0 and artinian

DimA rop5.8

Prop5.5 dim is local

Def 5.3 dimxX

Def 4.19 function field

Prop4.18 OX Ksi

Prop4.17 X intégral

SpecA integral iff A integral

Def 4.16 integral

Rmk4.15 X_P forms open?

Rmk4.14 OXy to OXx

Eg 4.13

Prop4.12 Orr compo of Spec OX,x

4.11 generic point

Prop4.9 noetherian scheme only finite Orr component

prop4.7 minimal prime

Prop4.5 irreducible of open subset is the intersection with

Irrreducib component

2.4.2 irreducibility

Prop4.2 reduced scheme

Def4.1 reduced scheme

3.50 X0 is dense

Subvatiety

Rmk 3.48 algebraic variety over k are exactly finite type over spec k

Def3.47 Alg variety

Prop3.46 noetherian

Recall closed subscheme

Def3.45 noetherian scheme

Cor3.44 rational of proj

clarify k-points and closed points

important pf eg3.32

Important eg 3.29 k-points

Def 3.28 k-points

Len 3.43

Def3.42 Proj B projective scheme

3.40 map of graded rings

3.39 P^n_A

3.38 Proj B A-scheme

3.36 spec B_(f)

3.35 D+g

3.35 V+I J

Q8 B+

2.3.3 def V+I

3.16

3.15

3.14

3.11

3.10

3.9

Cor3.8

Eg3.6