Dieudonne

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