TY - JOUR
T1 - Counterexamples to the tilting and (p,r)-filtration conjectures
AU - Bendel, Christopher P.
AU - Nakano, Daniel K.
AU - Pillen, Cornelius
AU - Sobaje, Paul
N1 - Publisher Copyright:
© 2019 Walter de Gruyter GmbH, Berlin/Boston.
PY - 2019
Y1 - 2019
N2 - In this paper the authors produce a projective indecomposable module for the Frobenius kernel of a simple algebraic group in characteristic p that is not the restriction of an indecomposable tilting module. This yields a counterexample to Donkin's longstanding Tilting Module Conjecture. The authors also produce a Weyl module that does not admit a p-Weyl filtration. This answers an old question of Jantzen, and also provides a counterexample to the (p, r) {(p,r)} -Filtration Conjecture.
AB - In this paper the authors produce a projective indecomposable module for the Frobenius kernel of a simple algebraic group in characteristic p that is not the restriction of an indecomposable tilting module. This yields a counterexample to Donkin's longstanding Tilting Module Conjecture. The authors also produce a Weyl module that does not admit a p-Weyl filtration. This answers an old question of Jantzen, and also provides a counterexample to the (p, r) {(p,r)} -Filtration Conjecture.
UR - http://www.scopus.com/inward/record.url?scp=85075728798&partnerID=8YFLogxK
U2 - 10.1515/crelle-2019-0036
DO - 10.1515/crelle-2019-0036
M3 - Article
AN - SCOPUS:85075728798
SN - 0075-4102
SP - 193
EP - 202
JO - Journal fur die Reine und Angewandte Mathematik
JF - Journal fur die Reine und Angewandte Mathematik
ER -