Spaces - Lecture $1$ - $12.04.2019$

Spaces - Lecture $2$ - $16.04.2019$

Sheaves on Grothendieck Topologies Toy Example

Spaces - Lecture $3$ - $23.04.2019$

$19.04.2019$ Friday - no lecture, because of official holidays Example $4$ is still not very clear to me. Maybe somebody can elaborate on this.

Spaces - Lecture $4$ - $26.04.2019$

Spaces - Lecture $5$ - $30.04.2019$

Spaces - Lecture $6$ - $03.05.2019$

Spaces - Lecture $7$ - $7.5.2019$

Spaces - Lecture $8$ - $10.05.2019$

Spaces - Lecture $9$ - $14.05.2019$

Example
Topos without points
</br> Real algebraic geometry
Bijection $(F^n)^*\overset{\sim}{\to} \operatorname{Sper}(R)$.

Spaces - Lecture $10$ - $17.05.2019$

Spaces - Lecture $11$ - $21.05.2019$

Spaces - Lecture $12$ - $24.05.2019$

Spaces - Lecture $13$ - $28.05.2019$

Spaces - Lecture $14$ - $31.05.2019$

Spaces - Lecture $15$ - $04.06.2019$

We dealt with properties of Tate rings, $f$-adic rings and adic rings as well as with Huber pairs. We constructed $A\langle T_1,\pts,T_n\rangle$ and $A\langle T\rangle$ where $A$ is a $nat$-ring. We gave universal properties for $A[T_1,\pts,T_n]$ and $A\langle T_1,\pts,T_n\rangle$. We gave an explicit description of $A\langle T\rangle$ and properties of $A[T_1,\pts, T_n]$ and $A\langle T_1,\pts,T_n\rangle$.

Spaces - Lecture $16$ - $07.06.2019$

Spaces - Lecture $17$ - $18.06.2019$

Proposition $8$
Corollary $2$

Spaces - Lecture $18$ - $21.06.2019$

$\bullet A\langle a^{\pm 1}\rangle\to B$ $\iff$ $A\to B, f(a)^{\pm 1}$ is power-bounded

spaces - Lecture $19$ - $25.06.2019$

Spaces - Lecture $20$ - $28.06.2019$

$\bullet$Definition
$\bullet\bullet$nat algebra topologically of finite type
$\bullet\bullet$affinoid algebra
$\bullet\bullet$ $\operatorname{Sp}(A)$

Spaces - Lecture $21$ - $02.07.2019$

Where is the beginning of this lecture?

Spaces - Lecture $22$ - $05.07.2019$

Spaces - Lecture $23$ - $09.07.2019$

Spaces - Lecture $24$ - $12.07.2019$

with no points

(This is still a bit sketchy and will be continued, just not sure when..Also all the necessary definitions will be given)