TY - JOUR
T1 - Local terms for the categorical trace
AU - Gaitsgory, Dennis
AU - Varshavsky, Yakov
N1 - Publisher Copyright:
© 2025 Elsevier Inc.
PY - 2025/6
Y1 - 2025/6
N2 - In this paper we introduce the categorical “true local terms” maps for Artin stacks and show that they are additive and commute with proper pushforwards, smooth pullbacks and specializations. In particular, we generalizing results of [14] to this setting. As an application, we supply proofs of two theorems stated in [1]. Namely, we show that the “true local terms” of the Frobenius endomorphism coincide with the “naive local terms” and that the “naive local terms” commute with !-pushforwards. The latter result is a categorical version of the classical Grothendieck–Lefschetz trace formula.
AB - In this paper we introduce the categorical “true local terms” maps for Artin stacks and show that they are additive and commute with proper pushforwards, smooth pullbacks and specializations. In particular, we generalizing results of [14] to this setting. As an application, we supply proofs of two theorems stated in [1]. Namely, we show that the “true local terms” of the Frobenius endomorphism coincide with the “naive local terms” and that the “naive local terms” commute with !-pushforwards. The latter result is a categorical version of the classical Grothendieck–Lefschetz trace formula.
KW - Categorical trace
KW - Lefshetz trace formula
KW - Local terms
UR - http://www.scopus.com/inward/record.url?scp=105001487085&partnerID=8YFLogxK
U2 - 10.1016/j.aim.2025.110223
DO - 10.1016/j.aim.2025.110223
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AN - SCOPUS:105001487085
SN - 0001-8708
VL - 470
JO - Advances in Mathematics
JF - Advances in Mathematics
M1 - 110223
ER -