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Introduction to plectic cohomology. (English) Zbl 1402.11092
Jiang, Dihua (ed.) et al., Advances in the theory of automorphic forms and their $$L$$-functions. Workshop in honor of James Cogdell’s 60th birthday, Erwin Schrödinger Institute (ESI), University of Vienna, Vienna, Austria, October 16–25, 2013. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-1709-3/pbk; 978-1-4704-3005-4/ebook). Contemporary Mathematics 664, 321-337 (2016).
Summary: We formulate conjectures on the existence of extra symmetries of the cohomology of Shimura varieties whose defining group is a restriction of scalars from a totally real field. We discuss evidence in its favour and potential arithmetic applications.
For the entire collection see [Zbl 1341.11002].

##### MSC:
 11G18 Arithmetic aspects of modular and Shimura varieties 14G35 Modular and Shimura varieties 14F43 Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies)
##### Keywords:
plectic cohomology
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