Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Points rationnels et groupes fondamentaux : applications de la
  cohomologie $p$-adique   In this talk, I report on three theorems concerning algebraic varieties over
a field of characteristic $p>0$. a) over a finite field of cardinal $q$, two
proper smooth varieties which are geometrically birational have the same number
of rational points modulo $q$ (cf. Ekedahl, 1983). b) over a finite field of
cardinal $q$, a proper smooth variety which is rationally chain connected, or
Fano, or weakly unirational, has a number of rational points congruent to 1
modulo $q$ (Esnault, 2003). c) over an algebraic closed field of caracteristic
$p>0$, the fundamental group of a proper smooth variety which is rationally
chain connected, or Fano, or weakly unirational, is a finite group of order
prime to $p$ (cf. Ekedahl, 1983). The common feature of the proofs is a control
of the $p$-adic valuations of Frobenius and is best explained within the
framework of Berthelot's rigid cohomology. I also explain its relevant
properties.

20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con