Coverings in p-adic analytic geometry and log coverings I: Cospecialization of the (p')-tempered fundamental group for a family of curves

Coverings in p-adic analytic geometry and log coverings II: Cospecialization of the p'-tempered fundamental group in higher dimensions

This paper constructs cospecialization homomorphisms between the (p') versions of the tempered fundamental group of the fibers of a smooth morphism with polystable reduction (the tempered fundamental group is a sort of analog of the topological fundamental group of complex algebraic varieties in the p-adic world). We studied the question for families of curves in another paper. To construct them, we will start by describing the pro-(p') tempered fundamental group of a smooth and proper variety with polystable reduction in terms of the reduction endowed with its log structure, thus defining tem…

Tempered fundamental group and metric graph of a Mumford curve

This paper is an attempt to give some general results on the tempered fundamental group of a $p$-adic smooth algebraic varieties (which is a sort of analog of the topologic fundamental group of complex algebraic varieties in the p-adic world). The main result asserts that one can recover the metric structure of the graph of the stable model of a Mumford curve from the tempered fundamental group of this Mumford curve. We will also prove birational invariance, invariance by algebraically closed extensions and a Kuenneth formula for the tempered fundamental group. We will describe the tempered fu…

Géométrie anabélienne tempérée

The tempered fundamental group of a p-adic analytic variety classifies étale coverings that become topological coverings (for the Berkovich topology) after finite étale base change. I study what can be recovered from the tempered fundamental group. In particular, I prove that, for a Mumford curve, one can recover the metric of the graph of the stable reduction from the tempered fundamental group. I also study how the tempered fundamental group behaves along the fibers of a fibration.

$p$-进ABV-包的Whittaker归一化与 tempered 表示的Vogan猜想

Whittaker normalization of $p$-adic ABV-packets and Vogan's conjecture for tempered representations

本研究证明$p$-进群ABV-包不依赖Whittaker基准选取，得出其到基本群映射的依赖关系，提出并证明拟分裂典型群ABV-包通有性猜想，验证开参数ABV-包为L-包，最终证明tempered表示的Vogan猜想。

回火圆盘与回火上同调

The tempered disk and the tempered cohomology

该研究基于完备离散赋值环，借助导出解析几何框架将\(V -\)概型一般纤维视为导出解析空间，引入回火管状邻域并定义回火德拉姆上同调，最终证明其与晶体上同调在光滑恰当\(k -\)概型上一致。

Untilts of fundamental groups: construction of labeled isomorphs of fundamental groups

I show that one can explicitly construct topologically/geometrically distinguishable data which provide isomorphic copies (i.e. \emph{isomorphs}) of the tempered fundamental group of a geometrically connected, smooth, quasi-projective variety over $p$-adic fields.