All Episodes

3.3

3.2

3.1

2.20

2.17

Thm2.16

2.15

A is dedekind then M is torsionfree iff flat

Dedekind

Prop2.3

2.12

Lemma 2.10/11

Q7 cor 2.9

2.7 Nakayama

Prop2.6

Cor 2.5

Thm 2.4

eg2.3

important 1.13 cf eg 2.3

2.2

2.1

1.14

1.9

1.8

1.8 u tensor v

1.7 multitensor

Cor 1.6 tensor with one free

BKS group

BdR/fil0

epi-mono decomposition

Exact equivalence? Étale phi gamma to lattice of reps

Exact Equivalence category; Galois reps and crystalline

exact equivalence p-adic Cris rep

Fundamental exc seq

Q4. Over N_F(T), Nyg fil

Q3. Exact equivalence between Isogeny category

Q2. What is [p]_q?

Q1 Gamma K Zp*

Eg3.39 define Projective space again by ProjB

P52. D+(f) iso to Spec B_(f)

P50. Def projective space.

P51. Def B_(f)

P51. Let f in B be a homogeneous element. D+(f) constitute a base.

Lemma 3.35 projB

Lemma 3.23 morphism to affine; k-rational pts are those k(x)=k.

prop. 3.20 closed immersion into affine is affine Spec A/I

Lemma 3.17 closed immersion from A to A/I; spec k(x) to X map to x;

Def 3.13 map of schemes Prop 3.14 ring maps gives scheme maps

Prop 3.12 X_f is open subset with O_X(X_f) iso O_X(X)_f

Lemma 3.7 D(g) of affine is affine

Eg. 3.4 some examples of O_X(U)

Lemma3.3 Spec A with A integral domain; O_X(U) injective into O_X,ksi

Def 3.2 define O_X by evaluating on D(f)

Prop 2.24 closed immersion

Def 2.19 ringed topological space; residue field k(x); local map

Lemma 2.16 stalk commutes with quotient and image (of sheaves)

Prop 2.12 iso iff stalk is iso

Def 2.10 surjective of presheaf is defined on all stalk, not on sections

Lemma2.9 stalk zero everywhere implies zero. Revisit direct limit

Rmk.2.6 a sheaf is completely determined by its section over a base of opens

E.g 2.4 constant pre-sheaf?

Def 2.1 sheaf

Prop1.19 recover idéal I from Z(I)

Cor 1.15 closed points of SpecA f.g k-alg and algebraic set Z(I) —— rational points of …

Cor1.13 describe maximal ideals of f.g Alg over k. (Weak Nullstellensatz)

Cor1.12 A/m is finite over k, if A is f.g k-alg

Prop1.9 Norther normalization

Eg1.8 SpecZ[T]

Lemma1.7 Liu

lemma 1.6 Liu

You#Ponj duality

P# 15 16 some details eqi of phi module with gallois rep

W#18 prism sit

W#12 13 Perf Tate ring; int perf tate

W#2 main Thm

W#1 abstract; equivalence phi gamma vs pris f-crystals

Alg#43 Limit colimit perfection

Pris Laurent F-crs

pd#3 mys functor

pd#1(III) F-crstl effective loc shtk z-crstl

pd#6 local stk vs Dieudonne mod

pd#1 F-crystals

3C# crystalline coho (II)

3C#6 crystalline coho (I)

CC#19 the construction of w_n (and ring A used to define it)

CC# H^1(K,V) and Ext^1(V,Zp)

诗篇100

CC#10 The proposition I.4.1 (ii) To prove the map sigma to c_{x,y}(sigma) from H^1(complex) to H^1(K,V) is an iso.

5#16 p-adic completion of polynomial (or power series) ring

5#17 frac field of power series ring over field? Local ring? General ring?

#2.20 III C[x,y,x]/(y-xz) as C[x,y]-module is not flat. (to modify)

#2.20 II (x,y) is not flat-C[x,y]

诗篇3

诗篇2

诗篇1

LG#14 Perfect p g module argument

诗篇127:1-2

#GF2

#4.80 etale map of schemes vs. etale extension of fields

#6.37