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Abstract Climate change poses significant threats to global agriculture, impacting food quantity, quality, and safety. The world is far from meeting crucial climate targets, prompting the exploration of alternative strategies such as stratospheric aerosol intervention (SAI) to reduce the impacts. This study investigates the potential impacts of SAI on rice and wheat production in India, a nation highly vulnerable to climate change given its substantial dependence on agriculture. We compare the results from the Assessing Responses and Impacts of Solar climate intervention on the Earth system with Stratospheric Aerosol Injection‐1.5°C (ARISE‐SAI‐1.5) experiment, which aims to keep global average surface air temperatures at 1.5°C above preindustrial in the Shared Socioeconomic Pathway 2‐4.5 (SSP2‐4.5) global warming scenario. Yield results show ARISE‐SAI‐1.5 leads to higher production for rainfed rice and wheat. We use 10 agroclimatic indices during the vegetative, reproductive, and ripening stages to evaluate these yield changes. ARISE‐SAI‐1.5 benefits rainfed wheat yields the most, compared to rice, due to its ability to prevent rising winter and spring temperatures while increasing wheat season precipitation. For rice, SSP2‐4.5 leads to many more warm extremes than the control period during all three growth stages and may cause a delay in the monsoon. ARISE‐SAI‐1.5 largely preserves monsoon rainfall, improving yields for rainfed rice in most regions. Even without the use of SAI, adaptation strategies such as adjusting planting dates could offer partial relief under SSP2‐4.5 if it is feasible to adjust established rice‐wheat cropping systems. 

Abstract Uttar Pradesh, with a population of 237 million, is the largest agrarian state in India, located in the Indo‐Gangetic plains. Rice cultivation is widespread across all districts of Uttar Pradesh, which have varying climate regimes, irrigation infrastructures, crop management practices, and farm sizes. The state is characterized by different agroecological zones (AEZs) with semi‐arid to sub‐humid climates with significant variability in monsoon rainfall. In this study, the impact of climate change on Kharif‐season rice is estimated using crop‐climate scenarios in Uttar Pradesh. A process‐based Crop Simulation Model, Crop Estimation through Resource and Environment Synthesis‐Rice, was simulated with bias‐corrected and downscaled climate data for historical (1995–2014) and three future periods (the 2030s, 2050s, and 2090s) for two mitigation pathways (SSP2‐4.5 and SSP5‐8.5) from the Coupled Model Intercomparison Project 6. Phenology, irrigation amount, crop evapotranspiration, yield, and water use efficiency were evaluated and assessed for all AEZs. Based on the ensemble of 16 climate models, rainfed rice yield increased in the AEZs of western Uttar Pradesh due to increased rainfall, while in eastern Uttar Pradesh yield decreased, under both shared socioeconomic pathways (SSPs). Irrigated rice yield decreased in all AEZs under both SSPs due to an increase in temperature and a decrease in the length of the growing period, with reductions of up to 20% by the 2090s. Irrigation requirements decreased from the 2030s to the 2090s due to increased rainfall and decreased crop evapotranspiration. Despite the projected increase in rainfed yield, the overall rice yield is expected to decrease in the future under both SSPs. 

We prove that if f f is a reduced homogeneous polynomial of degree d d , then its F F -pure threshold at the unique homogeneous maximal ideal is at least 1 d − 1 \frac {1}{d-1} . We show, furthermore, that its F F -pure threshold equals 1 d − 1 \frac {1}{d-1} if and only if f ∈ m [ q ] f\in \mathfrak m^{[q]} and d = q + 1 d=q+1 , where q q is a power of p p . Up to linear changes of coordinates (over a fixed algebraically closed field), we classify such “extremal singularities”, and show that there is at most one with isolated singularity. Finally, we indicate several ways in which the projective hypersurfaces defined by such forms are “extremal”, for example, in terms of the configurations of lines they can contain. 

Cubic surfaces in characteristic two are investigated from the point of view of prime characteristic commutative algebra. In particular, we prove that the non-Frobenius split cubic surfaces form a linear subspace of codimension four in the 19-dimensional space of all cubics, and that up to projective equivalence, there are finitely many non-Frobenius split cubic surfaces. We explicitly describe defining equations for each and characterize them as extremal in terms of configurations of lines on them. In particular, a (possibly singular) cubic surface in characteristic two fails to be Frobenius split if and only if no three lines on it form a “triangle”.