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過去の記録 ～07/27｜次回の予定｜今後の予定 07/28～
| 開催情報 | 金曜日 13:30～15:00 数理科学研究科棟(駒場) 118号室 |
|---|---|
| 担当者 | 權業 善範、河上 龍郎 、榎園 誠 |
次回の予定
2026年07月31日(金)
16:00-17:30 数理科学研究科棟(駒場) 118号室
Adrian Langer 氏 (University of Warsaw)
Fundamental group schemes in positive characteristic and its
applications
Adrian Langer 氏 (University of Warsaw)
Fundamental group schemes in positive characteristic and its
applications
[ 講演概要 ]
The main goal of this talk is to study analogues of the topological
fundamental group for (possibly singular) algebraic varieties in
positive characteristic. I will focus on one such analogue, whose
category of representations is given by crystals on so called stratified
site of a variety X.
This is motivated by Grothendieck's version of the Riemann-Hilbert
correspondence, which states that for a proper complex, possibly
singular, variety the category of representations of the topological
fundamental group of the analytification of X is equivalent to the
category of crystals on the stratified site of X. In positive
characteristic, crystals on the stratified site can equivalently be
described as F-divided bundles. For smooth varieties, these objects have
been studied extensively by, among others, D. Gieseker, J. P. dos
Santos, H. Esnault, V. Mehta and V. Srinivas. In this talk, I will
discuss several properties of the fundamental group that are familiar
from the complex setting and show that they continue to hold in positive
characteristic, even for singular varieties. As an application, I will
prove that simply connected, proper, normal varieties in positive
characteristic admit no nontrivial F-divided bundles. This generalizes
an earlier result of H. Esnault and V. Mehta concerning smooth
projective varieties, and settles Gieseker's conjecture in a more
general setting. If time permits I will also discuss the relative
version of Gieseker's conjecture. Most of this work is joint with Lei
Zhang (SYSU, Zhuhai).
The main goal of this talk is to study analogues of the topological
fundamental group for (possibly singular) algebraic varieties in
positive characteristic. I will focus on one such analogue, whose
category of representations is given by crystals on so called stratified
site of a variety X.
This is motivated by Grothendieck's version of the Riemann-Hilbert
correspondence, which states that for a proper complex, possibly
singular, variety the category of representations of the topological
fundamental group of the analytification of X is equivalent to the
category of crystals on the stratified site of X. In positive
characteristic, crystals on the stratified site can equivalently be
described as F-divided bundles. For smooth varieties, these objects have
been studied extensively by, among others, D. Gieseker, J. P. dos
Santos, H. Esnault, V. Mehta and V. Srinivas. In this talk, I will
discuss several properties of the fundamental group that are familiar
from the complex setting and show that they continue to hold in positive
characteristic, even for singular varieties. As an application, I will
prove that simply connected, proper, normal varieties in positive
characteristic admit no nontrivial F-divided bundles. This generalizes
an earlier result of H. Esnault and V. Mehta concerning smooth
projective varieties, and settles Gieseker's conjecture in a more
general setting. If time permits I will also discuss the relative
version of Gieseker's conjecture. Most of this work is joint with Lei
Zhang (SYSU, Zhuhai).
